Chapter 9.6, Problem 13E

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340

Chapter
Section

### Mathematical Applications for the ...

12th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781337625340
Textbook Problem

# Differentiate the functions in Problems 3-20. g ( x ) = 1 ( 2 x 3 + 3 x + 5 ) 3 / 4

To determine

To calculate: The derivative of the function g(x)=1(2x3+3x+5)3/4.

Explanation

Given Information:

The provided function is g(x)=1(2x3+3x+5)3/4.

Formula used:

Power rule for a real number n is such that, if y=un then dydx=nunâˆ’1â‹…dudx, where u is a differentiable function of x.

Power of x rule for function f(x)=xn is fâ€²(x)=nxnâˆ’1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=câ‹…u(x), where u(x) is a differentiable function of x, then fâ€²(x)=câ‹…uâ€²(x).

Constant function rule for a constant c is such that, if f(x)=c then fâ€²(x)=0.

If any nonzero real number a has a negative integer n as its exponent then aâˆ’n=1an.

Calculation:

Consider the function,

g(x)=1(2x3+3x+5)3/4

Rewrite the function as,

g(x)=(2x3+3x+5)âˆ’3/4

Consider (2x3+3x+5) to be u,

g(x)=uâˆ’3/4

Differentiate both sides with respect to x,

gâ€²(x)=ddx(uâˆ’3/4)

Simplify using the power rule,

gâ€²(x)=âˆ’34â‹…uâˆ’34âˆ’1â‹…dudx=âˆ’34uâˆ’7/4dudx

Substitute

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started