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Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

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BuyFindarrow_forward

Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem

Finding Derivatives In Exercises 41–56, find the derivative of the function. State which differentiation rule(s) you used to find the derivative.

f ( x ) = x ( 3 x 9 ) 3

To determine

To calculate: The derivative of the provided function f(x)=x(3x9)3.

Explanation

Given Information:

The provided function is f(x)=x(3x9)3.

Formula used:

Product rule of differentiation:

ddx[f(x)g(x)]=f(x)ddxg(x)+g(x)ddxf(x)

General power rule of differentiation:

ddx[f(x)]n=n[f(x)]n1f(x)

where f(x) is a differentiable function and n is an any real number.

Constant rule of differentiation:

ddx(c)=0

where c is a constant.

Simple power rule of differentiation:

ddxxn=nxn1

where x is a differentiable function and n is an any real number.

Constant multiple rule of differentiation:

ddxcv=cddx(v)

where c is constant.

Calculation:

Consider the function f(x)=x(3x9)3.

Differentiate the function f(x)=x(3x9)3 with respect to x.

Apply the property of product rule of differentiation,

dydx=ddxx(3x9)3=xddx(3x9)3+(3x9)3ddxx

Apply the property of general power rule of differentiation,

dydx=xddx

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