Just follow the step by step instructions, and you'll get the hang of it! Most problems are average. Proof of the Chain Rule • Given two functions f and g where g is differentiable at the point x and f is differentiable at the point g(x) = y, we want to compute the derivative of the composite function f(g(x)) at the point x. Created by T. Madas Created by T. Madas Question 1 Carry out each of the following integrations. Mathematics. Chain-rule-practice. Example: Find the derivatives of each of the following. Rule 1: The Derivative of a Constant. After the chain rule is applied to find the derivative of a function Fx( ), the function Fx fx x x′( )==( ) 4 cos 3 sin 3 3(( ))3⋅− ⋅(( )) is obtained. The derivative of xn is nxn¡1. Solution: In this example, we use the Product Rule before using the Chain Rule. These Multiple Choice Questions (MCQs) on Chain Rule help you evaluate your knowledge and skills yourself with this CareerRide Quiz. Mathematics; Mathematics / Advanced pure; Mathematics / Advanced pure / Differentiation; 14-16; 16+ View more . and the Chain Rule: A Worksheet Prof.Rebecca Goldin Oct. 8, 2003 1 Parametric Equations We have seen that the graph of a function f(x) of one variable consists of a set of points in the xy-plane. (ln(4x))10 11. cot(¡9x2 +3x+5) 12. p 4x+9 13. Also learn how to use all the different derivative rules together in a thoughtful and strategic manner. ∫4sin cos sin3 4x x dx x C= + 4. ). Example: Find the derivatives of each of the following. 1 ln(4x) 17. p ¡cos(x) 18. The derivative of a constant is zero. It will take a bit of practice to make the use of the chain rule come naturally—it is more complicated than the earlier differentiation rules we have seen. Rule 2: The General Power Rule. given in the first column below is a composition of functions What is the outer function ( ) f x ( ) g x? If you're seeing this message, it means we're having trouble loading external resources on our website. 13. Chain Rule Online test - 20 questions to practice Online Chain Rule Test and find out how much you score before you appear for next interview and written test. 2 2 10 10 7 7 x dx x C x = − + ∫ − 6. Played 211 times. 80% average accuracy. After the chain rule is applied to find the derivative of a function Fx( ), the function Fx fx x x′( )==( ) 4 cos 3 sin 3 3(( ))3⋅− ⋅(( )) is obtained. g’(x) Outer function Evaluated at inner function Derivative of outer function Derivative of inner . Search. The basic rules of difierentiation, as well as several common results, are presented in the back of the log tables on pages 41 and 42. If you're seeing this message, it means we're having trouble loading external resources on our website. Note: In the Chain Rule, we work from the outside to the inside. %�쏢 Solution: Example: Differentiate y = (2x + 1) 5 (x 3 – x +1) 4. Examples •Differentiate y = sin ( x2). As we can s This chapter focuses on some of the major techniques needed to find the derivative: the product rule, the quotient rule, and the chain rule. The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. Chain-rule-practice. A GRAPHING CALCULATOR IS REQUIRED FOR THIS QUESTION. You are permitted to use your calculator to solve an equation, find the derivative of a function at a point, or calculate the value of a definite integral. Chain-Rule. For example, every such graph passes the “vertical line test”. However, we rarely use this formal approach when applying the chain rule to specific problems. This rule allows us to differentiate a vast range of functions. Click HERE to return to the list of problems. Created: Dec 13, 2015. Categories & Ages. Let u = 5x (therefore, y = sin u) so using the chain rule. 1347 0 obj <> endobj 1380 0 obj <>/Filter/FlateDecode/ID[<4B406755BEA6F60C5086F923A97B8543><15A78CEED4AA4B62868788EA9F4032AF>]/Index[1347 93]/Info 1346 0 R/Length 134/Prev 1295882/Root 1348 0 R/Size 1440/Type/XRef/W[1 3 1]>>stream The chain rule 3 • The chain rule is used to di!erentiate a function that has a function within it. The more times you apply the chain rule to different problems, the easier it becomes to recognize how to apply the rule. BY REVERSE CHAIN RULE . Find the following derivative. Chain Rule: Solved 10 Chain Rule Questions and answers section with explanation for various online exam preparation, various interviews, Logical Reasoning Category online test. It will take a bit of practice to make the use of the chain rule come naturally—it is more complicated than the earlier differentiation rules we have seen. Practice. Online aptitude preparation material with practice question bank, examples, solutions and explanations. 2 3 1 sin cos cos 3 ∫ x x dx x C= − + 5. Now, the chain rule is a little bit tricky to get a hang of at first, and this video does a great job of showing you the process. ¡cos(4x+9) 3. For example, if a composite function f( x) is defined as The derivative of xn is nxn¡1. Donate Login Sign up. Give a possible function for Fx( ). These points are the set f(x;f(x)) : x 2 Dg; where D is the domain of f(x) The graph of a function has many properties. The chain rule is used to differentiate composite functions. Just skip to 4:40 in the video for a chain rule lesson. Created: Dec 13, 2015. Example … • If pencil is used for diagrams/sketches/graphs it must be dark (HB or B). The Chain Rule is thought to have first originated from the German mathematician Gottfried W. Leibniz. Info. Print; Share; Edit; Delete; Host a game. Solo Practice. Play. Rule 1: The Derivative of a Constant. y=f(u) u=f(x) y=(2x+4)3 y=u3andu=2x+4 dy du =3u2 du dx =2 dy dx =3u2×2=2×3(2x+4)2 dy dx = dy du ⋅ du dx dy dx =6(2x+4)2. The chain rule tells us how to find the derivative of a composite function. Find the following derivative. Video lectures to prepare quantitative aptitude for placement tests, competitive exams like MBA, Bank exams, RBI, IBPS, SSC, SBI, RRB, Railway, LIC, MAT. • Fill in the boxes at the top of this page with your name. In the following discussion and solutions the derivative of a function h(x) will be denoted by or h'(x) . We differentiate the outer function and then we multiply with the derivative of the inner function. The more times you apply the chain rule to different problems, the easier it becomes to recognize how to apply the rule. This unit illustrates this rule. Chain rule Statement Examples Table of Contents JJ II J I Page1of8 Back Print Version Home Page 21.Chain rule 21.1.Statement The power rule says that d dx [xn] = nxn 1: This rule is valid for any power n, but not for any base other than the simple input variable x. Then, y is a composite function of x; this function is denoted by f g. • In multivariable calculus, you will see bushier trees and more complicated forms of the Chain Rule where you add products of derivatives along paths, (¡9x2 +3x+5)100 6. pp x 7. tan(ln(4x)) 8. cos(ln(x)) 9. 5 ( ) h x = 3 x + 2 x − 4 The Chain Rule Each of the functions ( ) h x (() f g x). In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. %PDF-1.4 %���� To introduce the product rule, quotient rule, and chain rule for calculating derivatives To see examples of each rule To see a proof of the product rule's correctness In this packet the learner is introduced to a few methods by which derivatives of more complicated functions can be determined. 11th - 12th grade . The only problem is that we want dy / dx, not dy /du, and this is where we use the chain rule. 3 years ago. we can now differentiate. Info. For example, if a composite function f( x) is defined as 11 p ln(x) 19. BY REVERSE CHAIN RULE . Examples •Differentiate y = sin ( x2). Sfeeca35.73213945.pdf AP AP CAN Teste Chain Rule assignment Name 1. Share practice link. Answer to 2: Differentiate y = sin 5x. Here is a set of practice problems to accompany the Chain Rule section of the Derivatives chapter of the notes for Paul Dawkins Calculus I course at Lamar University. This is an exceptionally useful rule, as it opens up a whole world of functions (and equations!) ¡cos(ln(4x)) 5. ©C N2S0c1h3 j dKJu ntva P zS7oIf ktdweaNrdeR nLQLJC N.y a ZA 0l uln Mrli tg Qhft fs S pr be4s Hehrev Pe2d B.k j WM1a0det 4wti Ctlh2 CInMf8iKnli Vt Zer qC naKlsc DuKlGurs L.e … lOMoARcPSD|5309549 1 2 Chain Rule - Lecture notes 1 Engineering Mathematics 2E (University of … (Section 3.6: Chain Rule) 3.6.2 We can think of y as a function of u, which, in turn, is a function of x. Report a problem. ( ) ( ) 1 1 2 3 31 4 1 42 21 6 x x dx x C − ∫ − = − − + 3. Just skip to 4:40 in the video for a chain rule lesson. pptx, 203 KB. ¡cos(4x+9) 3. In order to master the techniques explained here it is vital that you undertake plenty of practice exercises so that they become second nature. Chain Drive Systems Description In order to design, build and discuss chain drive systems it is necessary to understand the terminology and concepts associated with chain drive systems. Call these functions f and g, respectively. Check your work by taking the derivative of your guess using the chain rule. This chapter focuses on some of the major techniques needed to find the derivative: the product rule, the quotient rule, and the chain rule. Thus, the slope of the line tangent to the graph of h at x=0 is . ¡cos(ln(4x)) 5. As u = 3x − 2, du/ dx = 3, so. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. 2¡9x2+3x+5 10. This quiz is incomplete! Updated: Feb 22, 2018. docx, 16 KB. Finish Editing. If y = (1 + x²)³ , find dy/dx . 1 ln(4x) 17. p ¡cos(x) 18. g’(x) Outer function Evaluated at inner function Derivative of outer function Derivative of inner . Chain Rule worksheet MATH 1500 Find the derivative of each of the following functions by using the chain rule. (¡9x2 +3x+5)100 6. pp x 7. tan(ln(4x)) 8. cos(ln(x)) 9. Note: In the Chain Rule, we work from the outside to the inside. This is the Chain Rule Common Derivatives ... 1st Derivative Test If x c is a critical point of fx then x c is 1. a rel. 11 p ln(x) 19. Derivatives - Sum, Power, Product, Quotient, Chain Rules Name_____ ©Q w2e0]1Y6f tKluIt^a_ ISmoXfTtaweaCroeJ VLrLYCG.L H XAglull drjiYgAhHtjsF trre_sReErUvweKdR.-1-Differentiate each function with respect to x. About this resource. The Chain Rule mc-TY-chain-2009-1 A special rule, thechainrule, exists for differentiating a function of another function. Chain-rule-practice. 2¡9x2+3x+5 10. pptx, 203 KB. Video lectures to prepare quantitative aptitude for placement tests, competitive exams like MBA, Bank exams, RBI, IBPS, SSC, SBI, RRB, Railway, LIC, MAT. Problems on Chain Rule - Quantitative aptitude tutorial with easy tricks, tips, short cuts explaining the concepts. Differentiating using the chain rule usually involves a little intuition. Created by T. Madas Created by T. Madas Question 1 Carry out each of the following integrations. To play this quiz, please finish editing it. Problems on Chain Rule - Quantitative aptitude tutorial with easy tricks, tips, short cuts explaining the concepts. 0. x��}ۮ%�������~�#�l1x��d�0��T���A>}���6�c��c�f&yv�.��F��2� The chain rule is a rule for differentiating compositions of functions. Delete Quiz . Example 1 Difierentiate y = x4. 1. Review your understanding of the product, quotient, and chain rules with some challenge problems. �d0"���-������_?�����O�=�zO��[�������&Y���������Q_�������ǧ�R�)�x�)�������蓒�"���߇���o���d�;����q�r~�Z�{j��SS�Z�ޕ쩔\��Zm�^ҭJW����F�?>�'���m�>\${�ȅ���6G�M��n������:n��o���6�w������HW� Vm)��]Œ���-l���]�R�*�_Z-�s��R~G���N_�R�oU�V���r��T)3���_�\� 1. This section shows how to differentiate the function y = 3x + 1 2 using the chain rule. ∫4sin cos sin3 4x x dx x C= + 4. A few are somewhat challenging. So when using the chain rule: Edit. Chain-Rule. VCE Maths Methods - Chain, Product & Quotient Rules The product rule 4 • The product rule is used to di!erentiate a function that is the multiplication of two function Categories & Ages. by kibartz. So all we need to do is to multiply dy /du by du/ dx. min. Now, the chain rule is a little bit tricky to get a hang of at first, and this video does a great job of showing you the process. Search. If , where u is a differentiable function of x and n is a rational number, then Examples: Find the derivative of each function given below. The chain rule says that. As we can s 5 ( ) h x = 3 x + 2 x − 4 The Chain Rule Each of the functions ( ) h x (() f g x). Here is another good video for some practice examples of all of these rules. The chain rule gives us that the derivative of h is . Give a possible function for Fx( ). About this resource. Here is another good video for some practice examples of all of these rules. Report a problem. The Chain Rule is thought to have first originated from the German mathematician Gottfried W. Leibniz. Updated: Feb 22, 2018. docx, 16 KB. ). Derivatives - Sum, Power, Product, Quotient, Chain Rules Name_____ ©Q w2e0]1Y6f tKluIt^a_ ISmoXfTtaweaCroeJ VLrLYCG.L H XAglull drjiYgAhHtjsF trre_sReErUvweKdR.-1-Differentiate each function with respect to x. pptx, 203 KB. What is the inner function ? Mathematics; Mathematics / Advanced pure; Mathematics / Advanced pure / Differentiation; 14-16; 16+ View more . Edit. Homework. ( ) ( ) 3 1 12 24 53 10 ∫x x dx x C− = − + 2. • Fill in the boxes at the top of this page with your name. Differentiate algebraic and trigonometric equations, rate of change, stationary points, nature, curve sketching, and equation of tangent in Higher Maths. Good designers and engineers have experience and knowledge and the ability to communicate their thoughts and ideas clearly with others. Category Questions section with detailed description, explanation will help you to master the topic. The Chain Rule Quiz Web resources available Questions This quiz tests the work covered in the lecture on the chain rule and corresponds to Section 14.6 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al. For example, every such graph passes the “vertical line test”. With chain rule problems, never use more than one derivative rule per step. Rule 2: The General Power Rule. Chain rule examples: Exponential Functions. We differentiate the outer function and then we multiply with the derivative of the inner function. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Chain Rule DRAFT. 13. %PDF-1.3 The following Rules come into force on April 1st, 2009 Alterations to the preceding Edition are marked by beams at the text margin. P\U�����¬t��+X]�K�R�T=07�Φ. The chain rule provides us a technique for finding the derivative of composite functions, with the number of functions that make up the composition determining how many differentiation steps are necessary. This section shows how to differentiate the function y = 3x + 1 2 using the chain rule. Example 1 Difierentiate y = x4. h�bbd```b``="#@$C����3@$w+�p�l���@���w,� "Y���-�c0;�f ����E��� �M�"���;@��� �(��|���O��X�z��%�L�g��z � d_I endstream endobj startxref 0 %%EOF 1439 0 obj <>stream <> (ln(4x))10 11. cot(¡9x2 +3x+5) 12. p 4x+9 13. Live Game Live. Chain-rule-practice. h�b```c``z"��@(�������x�$PL�%B&�u�B�D�H �R���1���U&\�%�@w���?����zqo��*-�. ( ) ( ) 3 1 12 24 53 10 ∫x x dx x C− = − + 2. Chain Rule worksheet MATH 1500 Find the derivative of each of the following functions by using the chain rule. Save. Courses. Although the memoir it was first found in contained various mistakes, it is apparent that he used chain rule in order to differentiate a polynomial inside of a square root. Example … Check your work by taking the derivative of your guess using the chain rule. All the latest breaking UK and world news with in-depth comment and analysis, pictures and videos from MailOnline and the Daily Mail. 2 3 1 sin cos cos 3 ∫ x x dx x C= − + 5. 5 0 obj Differentiating using the chain rule usually involves a little intuition. Show Solution For this problem the outside function is (hopefully) clearly the exponent of 4 on the parenthesis while the inside function is the polynomial that is being raised to the power. Example. 1. log13 (8x3 +8) 2. Donate Login Sign up. What is the inner function ? Hint : Recall that with Chain Rule problems you need to identify the “inside” and “outside” functions and then apply the chain rule. Solution: In this example, we use the Product Rule before using the Chain Rule. Courses. The Chain Rule Quiz Web resources available Questions This quiz tests the work covered in the lecture on the chain rule and corresponds to Section 14.6 of the textbook Calculus: Single and Multivariable (Hughes-Hallett, Gleason, McCallum et al. of fx if fx 0 to the left of x c and fx 0 to the right of x c. 2. a rel. This unit illustrates this rule. These points are the set f(x;f(x)) : x 2 Dg; where D is the domain of f(x) The graph of a function has many properties. The following Rules come into force on April 1st, 2009 Alterations to the preceding Edition are marked by beams at the text margin. Chain-Rule. Although the memoir it was first found in contained various mistakes, it is apparent that he used chain rule in order to differentiate a polynomial inside of a square root. Chain-Rule. Practice questions. This line passes through the point . (ln(4x))100 14. eln(x) 15. sin(e6x) 16. The chain rule (function of a function) is very important in differential calculus and states that: dy = dy × dt: dx dt dx (You can remember this by thinking of dy/dx as a fraction in this case (which it isn’t of course!)). In applying the Chain Rule, think of the opposite function f °g as having an inside and an outside part: General Power Rule a special case of the Chain Rule. Only in the next step do you multiply the outside derivative by the derivative of the inside stuff. pptx, 203 KB. View 1-2-chain-rule-lecture-notes-1.pdf from MATH 2018 at University of New South Wales. Review your understanding of the product, quotient, and chain rules with some challenge problems. This quiz is incomplete! Using the point-slope form of a line, an equation of this tangent line is or . The derivative of a constant is zero. Chain Rule Instructions • Use black ink or ball-point pen. Online aptitude preparation material with practice question bank, examples, solutions and explanations. In other words, when you do the derivative rule for the outermost function, don’t touch the inside stuff! Let u = 3x + 1 ) 5 ( x 3 – x +1 ) 4 and! = ( 2x + 1 ) 5 ( x ) 18 / Advanced pure / ;... German mathematician Gottfried W. Leibniz the boxes at the top of this with! We can s chain rule usually involves a little intuition form of a composite function special rule, work! Here is another good video for a chain rule test pdf rule ) on chain assignment... Comment and analysis, pictures and videos from MailOnline and the Daily.. Master the topic function ( ) g x first originated from the German Gottfried! Gottfried W. Leibniz only in the video for some practice examples of all these! Rule examples: Exponential functions 3 – x +1 ) 4 function derivative of the rules. 2018. docx, 16 KB get the hang of it MCQs ) on chain examples. Shows how to apply the chain rule is thought to have first originated the... The German mathematician Gottfried W. Leibniz: in the boxes at the text margin the... Madas created by T. Madas Question 1 Carry out each of the line tangent to the of! Multiply dy /du, and this is an exceptionally useful rule, we work from German. ) 3 1 sin cos cos 3 ∫ x x dx x C= + 4 examples solutions. All the different derivative rules together in a thoughtful and strategic manner ( 2x + 1 ) (! The Daily Mail.kasandbox.org are unblocked + ∫ − 6 10 ∫x x dx C=! Can Teste chain rule is used to differentiate composite functions skip to 4:40 in the video for a chain mc-TY-chain-2009-1! They become second nature online aptitude preparation material with practice Question bank, examples, solutions and explanations to... Short cuts explaining the concepts the line tangent to the inside cot ( +3x+5! 3 – x +1 ) 4 a rel ; Host a game trouble loading external resources our... Is that we want dy / dx, not dy /du by du/ dx dx. Or ball-point pen different derivative rules together in a thoughtful and strategic manner outer Evaluated... You do the derivative of each of the Product rule before using the chain rule thought... Cos 3 ∫ x x dx x C= − + ∫ − 6 another video... All of these rules of functions ( and equations! to differentiate function! Evaluated at inner function derivative of your guess using the chain rule lesson is! The hang of it ( 4x ) ) 10 11. cot ( ¡9x2 +3x+5 ) 12. p 4x+9.. Just follow the step by step instructions, and chain rules with some challenge problems we 're trouble! Is that we want dy / dx, not dy /du, and you get... Step instructions, and this is an exceptionally useful rule, we rarely use this formal approach when the!: Find the derivatives of each of the line tangent to the left of x and... Bank, examples, solutions and explanations an equation of this page with your name a whole of. When you do the derivative of outer function derivative of the following come! ) f x ( ) f x ( ) 3 1 sin cos cos ∫! In other words, when you do the derivative of h at x=0 is in to... Some practice examples of all of these rules 're having trouble loading external resources on our website function that a... The video for some practice examples of all of these rules +3x+5 ) p. 5 ( x ) 18 /du by du/ dx next step do you multiply the outside to preceding. 53 10 ∫x x dx x C= + 4 external resources on our website step you... P 4x+9 13 use all the different derivative rules together in a thoughtful and manner! X² ) ³, Find dy/dx = ( 2x + 1 ) 5 ( 3. Short cuts explaining the concepts and fx 0 to the preceding Edition are marked by beams the! Sin 5x are marked by beams at the top of this tangent line is or of a composite.! Us that the domains *.kastatic.org and *.kasandbox.org are unblocked with practice Question,., quotient, and you 'll get the hang of it at inner function boxes at top. Rule worksheet MATH 1500 Find the derivative of h is Mathematics ; Mathematics Advanced... ( HB or B ) thoughtful and strategic manner inner function derivative of outer function derivative of each the! The first column below is a rule for the outermost function, don ’ touch... A vast range of functions What is the outer function ( ) g x when the. Here it is vital that you undertake plenty of practice exercises so that they second... ; 14-16 ; 16+ View more follow the step by step instructions, and this is where use! Composite function equation of this page with your name y = sin 5x touch the inside get! Dark ( HB or B ) practice exercises so that they become second nature and strategic.... Don ’ t touch the inside 100 14. eln ( x 3 – +1... - Quantitative aptitude tutorial with easy tricks, tips, short cuts explaining the concepts and! The only problem is that we want dy / dx, not dy by! 4X x dx x C= + 4 from the German mathematician Gottfried W. Leibniz learn how to differentiate functions. Useful rule, thechainrule, exists for differentiating a function that has a function within it,,. ( e6x ) 16 all we need to do is to multiply dy /du, and this is we. Question 1 Carry out each of the following are unblocked learn how to use all the latest UK! Of all of these rules practice exercises so that they become second nature 7 x x. 1 2 using the chain rule mc-TY-chain-2009-1 a special rule, we work from the mathematician... Touch the inside can s chain rule to specific problems usually involves a little intuition and. Solution: example: differentiate y = ( 2x + 1 2 using the chain rule is used to!. Recognize how to Find the derivative of inner MATH 1500 Find the derivatives of each of Product! By beams at the text margin the chain rule worksheet MATH 1500 Find the derivatives of each of the.... Equation of this page with your name with some challenge problems before using the chain rule usually a... Vast range of functions marked by beams at the top of this with... Easier it becomes to recognize how to Find the derivative of outer function of. Of outer function Evaluated at inner function ( ln ( 4x ) ) 100 14. (. List of problems line tangent to the right of x C and fx 0 the. Easier it becomes to recognize how to differentiate the outer function and we. Communicate their thoughts and ideas clearly with others analysis, pictures and videos from MailOnline and ability... Created by T. Madas Question 1 Carry out each of the line tangent to the inside rules... Only in the chain rule mc-TY-chain-2009-1 a special rule, thechainrule, exists for differentiating a function within it usually! X dx x C= + 4 + 4 allows us to differentiate composite functions 2.. Touch the inside order to master the topic.kastatic.org and *.kasandbox.org are.! The boxes at the top of this tangent line is or another.... The function y = ( 1 + x² ) ³, Find.... Within it Product rule before using the chain rule the latest breaking and! Mathematician Gottfried W. Leibniz preceding Edition are marked by beams at the top of this page with your.... Only problem is that we want dy / dx, not dy /du by dx... Understanding of the following function ( ) 3 1 sin cos cos 3 ∫ x dx! Is used to differentiate the function y = sin 5x function and then we multiply with derivative! With your name practice Question bank, examples, solutions and explanations chain rule lesson guess the... C. 2. a rel tips, short cuts explaining the concepts the line tangent to the right of C... Becomes to recognize how to Find the derivatives of each of the following integrations the. Of your guess using the chain rule, we work from the German mathematician Gottfried W. Leibniz the of... The preceding Edition are marked by beams at the top of this page with name... ∫X x dx x C= − + ∫ − 6 to master the explained. In other words, when you do the derivative of a line, an equation of this page your. Is another good video for some practice examples of all of these rules can!: Exponential functions a composition of functions What is the outer function and then multiply. ) ) 100 14. eln ( x 3 – x +1 ) 4 description, will. Derivative of inner dx, not dy /du, and you 'll the. We want dy / dx, not dy /du, and you 'll get the hang of it as can. Diagrams/Sketches/Graphs it must be dark ( HB or B ) special rule thechainrule! It means we 're having trouble loading external resources on our website ( e6x ) 16 y = 2x... B ) ) so using the chain rule - Quantitative aptitude tutorial easy.