ok, so you should have typednow the chain rule is used to differentiate composite functions, that is, functions formed by plugging in one function into another. so for example, here, instead of just you have , so the function is plugged into . moreover, within that function is another composite function. we get by plugging in the function into , and again, we get by plugging in into
so as you see, we have to do the chain rule a lot of times here.
the rule says,
so to differentiate a composite function, you differentiate the outer function as if the inside function was a single variable. then, to compensate for the fact that it really wasn't a single variable, you multiply by the derivative of the inside function.
so here goes: