   Chapter 9.6, Problem 2E ### 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

# In Problems 1-4, find d y d u , d u d x ,  and  d y d x . y = u 4  and  u = x 2 4 x

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(

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### Find more solutions based on key concepts 