   Chapter 9.6, Problem 13E Mathematical Applications for the ...

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

Solutions

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=nun1dudx, where u is a differentiable function of 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.

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

Calculation:

Consider the function,

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

Rewrite the function as,

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

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

g(x)=u3/4

Differentiate both sides with respect to x,

g(x)=ddx(u3/4)

Simplify using the power rule,

g(x)=34u341dudx=34u7/4dudx

Substitute

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