What is the chain rule? when do I have to use it?

The chain rule is the technique used for differentiation when the equation you're trying to differentiate contains a function of a function. Consider ln(x). You should know this differentiates to 1/x. If however we had to differentiate ln(3x) you may intuitively guess that this would differentiate to 1/3x. Using the chain rule we can see this is not the case. So, we have y = ln(3x). We want to find dy/dx. We know this can be treated as a fraction, and split it into dy/du du/dx. Now if we substitute u = 3x, y = ln(u), so dy/du = 1/u, du/dx = 3, so dy/dudu/dx = 3/u. Resubstitute u = 3x, and you get dy/dx = 3/3x = 1/x.