This shortcut is a little more complicated that the ones on the previous page. It is called the Product Rule.

$$ f'(  f(x)  g(x)  ) =  { f(x)   f'( g(x) )  +  g(x)   f'( f(x) ) } $$

The derivative of the product of two functions is the first function times the derivative of the second, plus the second function times the derivative of the first.