Derivative word problem: interpret dH/dv, for H(v) = ....

[AGlas9837]

At 0 degrees Celsius, the heat loss H (in kilocalories per square meter per hour) from a person's body can be modeled by:

H = 33(10(square root of v) - v + 10.45) where v is the wind speed (in meters per second).

I am asked (a) to find dH/dv and interpret its meaning in this situation; and (b) find the rates of change of H when v = 2 and when v = 5.

Since this is a derivative problem, I know I need to rewrite the square root of v as v to the 1/2 power. Within the equation, if I multiply v to the 1/2 power x 10, I get 5v and:

H = 33(5v - v + 10.45)

which doesn't make since because if I took the derivative of this, I wouldn't have a variable. What am I doing wrong?

 

[pka]

Re: Derivative word problem

\(\displaystyle \begin{array}{l} H = 33\left( {10\sqrt v - v + 10.4} \right) \\ \frac{{dH}}{{dv}} = 33\left( {\frac{5}{{\sqrt v }} - 1} \right) \\ \end{array}\)