Explanation Given: The function, y = e x . 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 d d x ( e x ) = e x 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 = e x 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 ) = x and outer function as y = f ( u ) = e u , because the composition of these functions gives y = f ( u ) = e u = e x Thus, theinner function is u = g ( x ) = x and y = f ( u ) = e u

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ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 3.5, Problem 5E

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To write thefunction y=ex 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 3.5, Problem 4E

Chapter 3.5, Problem 6E

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Chapter 3 Solutions

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To write thefunction y = e x 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=esqrtx as the composition of inner function and outer function.

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To write thefunction y=ex 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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