   Chapter 2.5, Problem 1E

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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 = 1 + 4 x 3

To determine

To write:

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

Explanation

Rules:

a) Constant function rule: ddx(c)=0

b) Power function rule: ddx(xn)=nxn-1

c) Constant multiple rule: ddx(Cf(x))=Cddx(f(x))

d) Difference rule: ddx(fx-g(x))=ddx(f(x))-ddx(g(x))

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

Given:

y= 1+4x3

Calculation:

Express y=fogx=f(gx) where y=fu= u3 and u=g

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