ordinarily, partial derivatives are used for functions of more than one independent variable because if you think of the derivative as a slope, then for functions of more than one variable, it is easiest to work with slopes in the direction of each of the coordinate axes (just as it is in the (simplest) case of a function of one variable, like y=f(x)). the partial derivatives just give you the slopes in the direction of each of the axes. however, there are ways to combine these partial derivatives to give a single entity (vector, matrix, etc.) that represents the derivative of your multivariable function.
