How do we find the derivative of a function that's made of one function nested inside another, like
esin x
or
(ln x)42?
The tool we need is called the Chain Rule. While the chain rule isn't always likeable at first, it grows on you. Once we've got the chain rule, we can also do something called implicit differentiation, which allows us to say some things about a function's derivative even if we aren't given a formula for that function. Clearly, our derivatives toolbox is growing.