Question

What is the partial derivative of a given function

Answer 1

Partial differentiation of a function with more than one variables refers to its derivative being taken with respect to one of those variables, while the rest being held as a constant.

An example is the volume of a cylinder given by:
$V(h, r) = \pi r^{2}h$

The volume requires two variables in order to work out the volume, namely the radius and the height.

Using partial differentiation, its partial derivative can become:
$\frac{\partial V}{\partial r} = 2\pi rh$

This symbol is used in place of the derivative symbol, in order to distinguish total derivatives and partial derivatives.