I'm trying to understand why you keep certain variables constant when taking partial derivatives. For example, for a function f(x,y), to take the partial derivative of f with respect to y, you "consider" x a constant and take the normal derivative with respect to 'y'.

In single variable calculus, the underlying idea of derivatives involve limits. The algorithm, to which I generally refer for example, would be "nx^(n-1)" for the derivative of x^n.

I'm hoping that if I know the reason behind the algorithm, I can understand what it geometrically means when keeping other variables constant.