Question

What are partial derivatives?

Answer 1

Hello,

If `f` is a function with 2 variables, for example

`f(x,y) = x^2y + \cos(xy)`

you can calculate 2 derivatives :

1) the derivative on `x` (then `y` is like a constant) : `f'_x(x,y)` or `\frac{\partial f}{\partial x}(x,y)`.

2) the derivative on `y` (then `x` is like a constant) : `f'_y(x,y)` or `\frac{\partial f}{\partial y}(x,y)`.

For example, with `f(x,y) = x^2y + \cos(xy)`, you have

`\frac{\partial f}{\partial x}(x,y) = 2xy - y\sin(xy)` and

`\frac{\partial f}{\partial y}(x,y) = x^2 - x\sin(xy)`.