Chapter 9.6, Problem 19E

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. 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)5âˆ’3w7.

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.

Calculation:

Consider the function,

z=(3w+1)5âˆ’3w7

Rearrange the function as,

z=(3w+1)57âˆ’37w

Consider (3w+1) to be u,

z=u57âˆ’37w

Differentiate both sides with respect to w,

dzdw=ddw(u57âˆ’37w)zâ€²=ddw(17u5)âˆ’ddw(37w)=17ddw(u5

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