   Chapter 9.6, Problem 21E ### 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. z = ( 3 w + 1 ) 5 − 3 w 7

To determine

To calculate: The derivative of the function z=(3w+1)53w7.

Explanation

Given Information:

The provided function is z=(3w+1)53w7.

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,

z=(3w+1)53w7

Rearrange the function as,

z=(3w+1)5737w

Consider (3w+1) to be u,

z=u5737w

Differentiate both sides with respect to w,

dzdw=ddw(u5737w)z=ddw(17u5)ddw(37w)=17ddw(u5

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