Chapter 9.6, Problem 47E

### 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

# Body-heat loss The description of body-heat loss due to convection involves a coefficient of convection, K c , which depends on wind velocity according to the following equation. K c = 4 4 v + 1 Find the rate of change of the coefficient with respect to the wind velocity.

To determine

To calculate: The rate of change of the coefficient with respect to the wind velocity. The description of body-heat loss due to convection involves a coefficient of convection, Kc, which depends on wind velocity according to the equation Kc=44v+1.

Explanation

Given Information:

The provided function is Kc=44v+1.

Formula used:

The power rule of differentiation,

ddxxn=nxnâˆ’1

Calculation:

Consider the provided function,

Kc=44v+1

Consider (4v+1) to be u,

Kc=4u=4u1/2

Differentiate both sides with respect to v,

dKcdv=ddv(4u1/2)

Simplify using the power rule,

dKcdv=4ddv(u1/2)dudv=4â‹…12u12âˆ’1dudv=2uâˆ’1/2dudv

Substitute (4v+1) for u,

d

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