   Chapter 9.6, Problem 2E 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

In Problems 1 and 2, find (b)  y = u 10  and  u = x 2 + 5 x . (a)  y = u 4  and  u = x 2 + 4 x (b)  y = u 10  and  u = x 2 + 5 x

(a)

To determine

To calculate: The derivative dydu,dudx and dydx for the functions y=u4 and u=x2+4x.

Explanation

Given Information:

The provided functions are y=u4 and u=x2+4x.

Formula used:

Power rule:

If y=un and u is differentiable function of x, then,

dydx=nun1dudx

According to the property of differentiation, if a function is of the form f(x)=u(x)+v(x), then,

f(x)=u(x)+v(x)

Calculation:

Consider the provided functions,

y=u4 And u=x2+4x

To find dydu differentiate both sides of the function y=u4 with respect to u,

dydu=ddu(u4)

Simplify using the power rule,

dydu=4u41=4u3

To find dudx differentiate both sides of the function u=x2+4x with respect to x,

dudx=ddx(x2+4x)=ddx(x2)+ddx(4x)=ddx(

(b)

To determine

To calculate: The derivative dydu,dudx and dydx for the functions y=u10 and u=x2+5x.

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