# What is the derivative of the work function?

It depends with respect to what physical quantity you're differentiating.

If you consider the derivative with respect to time, it is the power, by definition:

$P = \frac{\mathrm{dW}}{\mathrm{dt}}$

If you consider the derivative of the work with respect to position, we have the following result, using the Fundamental Theorem of Calculus:

$\frac{\mathrm{dW}}{\mathrm{dx}} = \frac{d}{\mathrm{dx}} {\int}_{a}^{x} F \left({x}^{p} r i m e\right) {\mathrm{dx}}^{p} r i m e = F \left(x\right)$

Which is the force.

This last result can be generalized to higher dimensions, as long as the force is conservative.