   Chapter 2.5, Problem 6E

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# Write the composite function in the form f ( g ( x ) ) . [Identify the inner function u = g ( x ) and the outer function y = f ( u ) .] Then find the derivative d y / d x . y = sin x

To determine

To write:

The composite function in the form of f(g(x)) and find dy/dx

Explanation

Formula:

i. d(x)dx=12x

ii. ddxsinx=cosx

Rules:

a) Chain rule: If Fx=fogx=fgx then F'x=f'gx*g'(x)

Given:

y=sinx

Calculation:

Express y=fogx=f(gx) where y=fu=sinu  and u=gx=x

Since

f'(u)=dfdu=<

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