Partial Derivatives

Partial derivatives are in many ways the same thing as a regular derivative, but for multivariate functions. The partial derivative of a function \(f\) with respect to an argument \(x\) is denoted by \(\frac{\partial f}{\partial x}\). One holds each of the other variables (those not in the derivative) constant in the function and takes the derivative in a regular fashion. Partial derivatives describe how much an infinitesmal change in one variable influences the overall change of the function. As a result, these are very useful in fields like machine learning and science.

EXAMPLE

\(f(x,y) = e^{2y}\sin{x}\)
To find \(\frac{\partial f}{\partial x}\) one would hold \(y\) constant and proceed as normal.
\(\frac{\partial f}{\partial x} f(x,y) = e^{2y}\cos{x}\)