Partial Derivative

A partial derivative is a function’s derivative with respect to one of those variables, while keeping all other variables constant.

For example, the partial derivative may be used to measure the slope of a function at the y or x axis in the case of a function $f(x,y)$.

Example

For function $f(x,y)=x^{2}y$, computing a partial derivative would look like the following: $\frac{\partial f}{\partial x}=\frac{\partial }{\partial x}{x}^{2}y=2xy$

In the above example, since we take the partial of x, we can treat y as a constant and take the $\text{derivative}$ of x.

$\frac{\partial f}{\partial y}=\frac{\partial }{\partial y}{x}^{2}y=x^2\ast 1$

Similarly, when we take the partial of y, we can treat x as a constant and take the $\text{derivative}$ of y.

When performing this operation, we may see how the function changes while allowing one variable to change, and holding all other variables constant.

#seed