   Chapter 9.7, Problem 22E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Find the derivatives of the functions in Problems 1-32. Simplify and express the answer using positive exponents only. c ( x ) = [ x 3 ( x 2 + 1 ) ] − 3

To determine

To calculate: The simplified form of the derivative of the function c(x)=[x3(x2+1)]3.

Explanation

Given Information:

The provided function is c(x)=[x3(x2+1)]3.

Formula used:

Power rule for a real number n is such that, if y=un then dydx=nun1dudx, where u is a differentiable function of x.

Product rule for function f(x)=u(x)v(x), where u and v are differentiable functions of x, then f(x)=u(x)v(x)+v(x)u(x).

Power of x rule for function f(x)=xn is f(x)=nxn1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=cu(x), where u(x) is a differentiable function of x, then f(x)=cu(x).

Constant function rule for a constant c is such that, if f(x)=c then f(x)=0.

Calculation:

Consider the function, c(x)=[x3(x2+1)]3

Consider x3(x2+1) to be u,

c(x)=u3

Differentiate both sides with respect to x,

c(x)=ddx(u3)

Use the power rule,

c(x)=3u31dudx=3u4dudx

Substitute x3(x2+1)</

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