I have a derivative question.
If "p" is price and "q" is quantity, and the demand for a product is q = 5000e(-0.08p) (exponential function), what is the derivative of demand with respect to price when p=$10. Interpret answer in terms of demand.

The derivative of a function like


y = Ae^{bx}


is:


\frac { dy} {dx}= Abe^{bx} = by


For your function you have p as the independent variable rather than x, A = 5000 and b = -0.08. Can you finish it from here?

I thought that the answer might be: q'= -400e (-.08 x 10) = -179.73. Am I doing the derivative wrong?

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You have it correct: the derivative at p = 10 is indeed dp/dq = -179.73 units/dollar.