What is the chain rule?

The chain rule is a rule that is used when calculating the derivative of a function. If you have a function within a function, i.e. f(g(x)), then the derivative is calculated as follows: df/dx = (df/dg)(dg/dx). It's easiest understood with an example: let's try to differentiate f(x)=sin(2x²). Here, g=2x² , and f(x) can be written in the form f(g)=sin(g). df/dg= cos(g), and dg/dx = 4x, using the power rule. So overall, df/dx = (df/dg)(dg/dx) = cos(g)4x= 4xcos(2x²), using the fact that g=2x² . The process can be repeated for multiple nested functions, i.e. for something like f(g(h(x))), df/dx=(df/dg)(dg/dh)*(dh/dx)