   Chapter 9.6, Problem 4E ### 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 10  and  u = x 2 + 5 x

To determine

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

Explanation

Given Information:

The provided functions are y=u10 and u=x2+5x.

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=u10 and u=x2+5x

To find dydu differentiate both sides of the function y=u10 with respect to u,

dydu=ddu(u10)

Simplify using the power rule,

dydu=10u101=10u9

To find dudx differentiate both sides of the function u=x2+5x with respect to x,

dudx=ddx(x2+5x)=ddx(x2)+ddx(5x)

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