How do I use the chain rule for differentiation?

The chain rule is used when we have a function in the form f(g(x)).

For example sin(x^3). [In this case, f(x) = sin(x) and g(x) = x^3]

The chain rule says that the derivative of f(g(x)) is g'(x)*f'(g(x)). 

For our example:

g'(x) = 3x^2 and f'(x) = cos(x). So the derivative will be 3x^2*cos(x^3).