Derivatives 101: what does "with respect to" mean? I'm studying derivatives 101 and I can't get my head around the phrasing "with respect to" something. 
Eg in chain rule we calculate the derivative of outer function with respect to inner + derivative of inner with respect to x. But what does it actually mean (in human language) to say a derivative is "with respect to" anything at all?
Thanks a ton.

You need to specify with respect to what in case there are several possibilities. This may arise with functions of several variables. It also arises in the context of the chain rule.
Consider $f(g(x))$ and differentiate:
$$\frac{df}{dx}=\frac{df}{dg}\frac{dg}{dx}.$$
This reads "the derivative of $f$ wrt $x$ is the product of the derivative of $f$ wrt $g$ and the derivative of $g$ (wrt to $x$ is implied).
