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Math
Mathematical Applications for the Management, Life, and Social Sciences11th Edition

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Chapter 9.6, Problem 15E
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Mathematical Applications for the ...

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

Solutions

Chapter
Section
Problem 1CP
Problem 2CP
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
BuyFindarrow_forward

Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
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=nun−1⋅dudx, where u is a differentiable function of x.

Power of x rule for function f(x)=xn is f′(x)=nxn−1, where n is a real number.

Coefficient rule for a constant c is such that, if f(x)=c⋅u(x), where u(x) is a differentiable function of x, then f′(x)=c⋅u′(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 a−n=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)=u−3/4

Differentiate both sides with respect to x,

g′(x)=ddx(u−3/4)

Simplify using the power rule,

g′(x)=−34⋅u−34−1⋅dudx=−34u−7/4dudx

Substitute

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