How to do the chain rule.

The chain rule is used for functions 'inside' other functions. We have learnt to differentiate functions like x^2, y^20, e^x, -sin(x), and we will use these results in the chain rule. Let's look at an example, f(x) = (2x+1)^(1/3). Notice how we have a function (2x+1) 'inside' of another function (u^(1/3)). The chain rule says that if we have a function f(u) in terms of a function u(x) then df/dx=df/dudu/dx, in other words we differentiate the outside and multiply it by the derivative of the inside. In our example f(u) = u^(1/3) and u(x) = 2x+1. Then df/du = 1/3u^(-2/3) = 1/3*(2x+1)^(-2/3) and du/dx = 2. So df/dx = 21/3(2x+1)^(-2/3)