\circ g)'(x) = \frac{d}{dx}(f\circ g)(x) =
    f'(g(x))\cdot g'(x).$$
  </div>Some people remember the theorem above as &ldquo;the
  derivative of a composition is the derivative of the outside
  (evaluated at the inside) multiplied by the derivative of the
  inside.&rdquo; If $u=g(x)$, we sometimes write $\ds
  \frac{df}{dx}=\frac{df}{du}\frac{du}{dx}$. The following problem
  should help us master this notation.

  <div class="problem" id="chain-rule-review-problem">
    Suppose we know that $\ds
    f'(x