How do you differentiate using the chain rule?

The chain rule is used where the equation you are looking to differentiate is a function that is itself raised to a power. For example, we might have y = (x²-2)³ and want to differentiate with respect to x to give dy/dx = ?We could multiply this out to give a full equation, but this can be messy especially if the outside power (3 in the above example) is high. Instead, we use the chain rule to give us a simpler way of working out the answer.What we will do is say u = x² - 2, meaning that y = u² we now differentiate y with respect to u, so:dy/du = 2uNext, we want to differentiate u with respect to x, so:du/dx = 2xNow, we can neatly combine the two, as (dy/du) * (du/dx) = dy/dx in the same way that it would with a normal fraction.So, dy/dx = 2u * 2xFinally, we want to have this only in terms of x, so we substitute back in the u equation we established to start with.Giving dy/dx = 4x * (x² - 2)