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3. Method A. Use the rule: y=u4/3 and u=3x²-1. Find dy du dy two ways. dx dy dy du = First find and separately, then multiply. dx du dx du dx y=u4/3, dy = du du u = 3x²-1 = dx Now multiply: dy dy du = = (In terms of u and x) dx du dx Now clean up by composing with the definition of u = 3x²-1 so that the derivative is given completely in terms of x. dy dx (only in terms of x) Method B. This time, do the problem a different way. First write y completely in terms of x by performing a composition. Then use the chain rule to find dy dx I.e. take the derivative of y=(3x²-1) 4/3 using the chain rule. c. You should get the same answer each way. If not, find your error and correct it. HW Supplement: Chain Rule 1. Find the derivative of f(x)= = a. First use the quotient rule. Name 2 3 x² +5 in two ways. Simplify each answer. b. Use the chain rule after rewriting f(x) as f(x)=3(x²+5)-1 Of course you should have the same answer for both. If not, find and correct your error. Which method do you prefer and why? (Over)

3. Method A. Use the rule: y=u4/3 and u=3x²-1. Find dy du dy two ways. dx dy dy du = First find and separately, then multiply. dx du dx du dx y=u4/3, dy = du du u = 3x²-1 = dx Now multiply: dy dy du = = (In terms of u and x) dx du dx Now clean up by composing with the definition of u = 3x²-1 so that the derivative is given completely in terms of x. dy dx (only in terms of x) Method B. This time, do the problem a different way. First write y completely in terms of x by performing a composition. Then use the chain rule to find dy dx I.e. take the derivative of y=(3x²-1) 4/3 using the chain rule. c. You should get the same answer each way. If not, find your error and correct it. HW Supplement: Chain Rule 1. Find the derivative of f(x)= = a. First use the quotient rule. Name 2 3 x² +5 in two ways. Simplify each answer. b. Use the chain rule after rewriting f(x) as f(x)=3(x²+5)-1 Of course you should have the same answer for both. If not, find and correct your error. Which method do you prefer and why? (Over)

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 94E
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3. Method A. Use the rule: y=u4/3 and u=3x²-1. Find dy du dy two ways. dx dy dy du = First find and separately, then multiply. dx du dx du dx y=u4/3, dy = du du u = 3x²-1 = dx Now multiply: dy dy du = = (In terms of u and x) dx du dx Now clean up by composing with the definition of u = 3x²-1 so that the derivative is given completely in terms of x. dy dx (only in terms of x) Method B. This time, do the problem a different way. First write y completely in terms of x by performing a composition. Then use the chain rule to find dy dx I.e. take the derivative of y=(3x²-1) 4/3 using the chain rule. c. You should get the same answer each way. If not, find your error and correct it.
Transcribed Image Text:3. Method A. Use the rule: y=u4/3 and u=3x²-1. Find dy du dy two ways. dx dy dy du = First find and separately, then multiply. dx du dx du dx y=u4/3, dy = du du u = 3x²-1 = dx Now multiply: dy dy du = = (In terms of u and x) dx du dx Now clean up by composing with the definition of u = 3x²-1 so that the derivative is given completely in terms of x. dy dx (only in terms of x) Method B. This time, do the problem a different way. First write y completely in terms of x by performing a composition. Then use the chain rule to find dy dx I.e. take the derivative of y=(3x²-1) 4/3 using the chain rule. c. You should get the same answer each way. If not, find your error and correct it.
HW Supplement: Chain Rule 1. Find the derivative of f(x)= = a. First use the quotient rule. Name 2 3 x² +5 in two ways. Simplify each answer. b. Use the chain rule after rewriting f(x) as f(x)=3(x²+5)-1 Of course you should have the same answer for both. If not, find and correct your error. Which method do you prefer and why? (Over)
Transcribed Image Text:HW Supplement: Chain Rule 1. Find the derivative of f(x)= = a. First use the quotient rule. Name 2 3 x² +5 in two ways. Simplify each answer. b. Use the chain rule after rewriting f(x) as f(x)=3(x²+5)-1 Of course you should have the same answer for both. If not, find and correct your error. Which method do you prefer and why? (Over)
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