Don't let Leibniz's notation scare you. Whether you write

or f'(x), it's just the derivative of f.

Your professor introduced a new variable (or a new function, depending on how you look at it)

. So

, and you take the derivative of both sides. The right side is easy. On the left, since w is a function of x, you have a composite function (

is

), so you need to use the chain rule. The derivative of the outside function is

, and the derivative of the inside function is

. So you have

, so

, and since

,

, which is what you wanted to show.

If you can't figure out the derivation, you should at least memorize the result

. Or in the other notation, if

,

.

Hope that helps.

- Hollywood