What are partial derivatives?

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Answer 1 · 2015-02-19T17:17:36

Hello,

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

$f (x, y) = x^{2} y + cos (x y)$ $f(x,y) = x^2y + \cos(xy)$

you can calculate 2 derivatives :

1) the derivative on $x$ $x$ (then $y$ $y$ 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

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