   Chapter 9.6, Problem 19E ### 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

# Differentiate the functions in Problems 3-20. y = 11 ( x 3 − 7 ) 6 9

To determine

To calculate: The derivative of the function y=11(x37)69.

Explanation

Given Information:

The provided function is y=11(x37)69.

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.

Calculation:

Consider the function, y=11(x37)69

Consider (x37) to be u,

y=119u6

Differentiate both sides with respect to x,

y=ddx(119u6)=119ddx(u6)

Use the power rule,

y

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