(C) 2012-2013 David Liao (lookatphysics.com)
One way to combine basic functions in more sophisticated structures is to nest functions sequentially within each other. This is called "composition of functions." The chain rule is used to study the slopes of composite functions. The rule is written d(g(f(x))/dx = dg(f(x))/df(x) df(x)/dx or d(g(f))/dx = dg/df df/dx and memorized using the mnemonic, "derivative of a function with an outside and an inside is derivative of the outside times derivative of the inside."