   Chapter 9.6, Problem 3E ### 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 = 4 x 2 − x + 8

To determine

To calculate: The derivative dydu,dudx and dydx for the functions y=u4 and u=4x2x+8.

Explanation

Given Information:

The provided functions are y=u4 and u=4x2x+8.

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=4x2x+8

To find dydu differentiate both sides of the function 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=4x2x+8 with respect to x,

dudx=ddx(4x2x+8)=ddx(4x2)ddx(x)+ddx(1)=4ddx<

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