Explanation Given: The function, y = ( 2 x 3 + 5 ) 4 . Concept Used: The composition function f ∘ g can be found by replacing x by g ( x ) in the function f ( x ) Chain rule, d d x ( f ( g ( x ) ) ) = f ' ( g ( x ) ) ⋅ g ' ( x ) Power rule of derivatives, d d x ( x n ) = n x n − 1 Derivative of any constant C is zero, that is, d d x ( C ) = 0 Exponent rule: a n = a 1 / n Calculation: In order to express the given function y = ( 2 x 3 + 5 ) 4 as the composition of inner function u = g ( x ) and the outer function y = f ( u ) , observe that the inner function can be taken as u = g ( x ) = 2 x 3 + 5 and outer function as y = f ( u ) = u 4 , because the composition of these functions gives y = f ( u )</

15th Edition

ISBN: 9781305177291

Author: James Stewart, Troy Day

Publisher: Cengage Learning

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Question

Chapter 3.5, Problem 2E

To determine

To write thefunction y=(2x3+5)4 as the composition of inner function u=g(x) and the outer function y=f(u) . And find the derivative dydx .

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Chapter 3 Solutions

Biocalculus: Calculus For Life Sciences

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To write thefunction y = ( 2 x 3 + 5 ) 4 as the composition of inner function u = g ( x ) and the outer function y = f ( u ) . And find the derivative d y d x .

Solution Summary: The author explains how to express the given function y=(2x3+5)4 as the composition of inner function and outer function.

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To write thefunction y=(2x3+5)4 as the composition of inner function u=g(x) and the outer function y=f(u) . And find the derivative dydx .

Chapter 3 Solutions