\[ h(x) = -\frac{1}{4}x^4 + \frac{2}{3}x^3 + 2x^2 - \sqrt{2}x + \pi^e \]

\begin{align*}
  h'(x) &= 4 \cdot -\frac{1}{4}x^{4-1} + 3 \cdot \frac{2}{3}x^{3-1} + 2\cdot2x^{2-1} - 1 \cdot \sqrt{2}x^{1-1} + 0 \cdot \pi^e x^{0-1} \\
  &= -x^{3} + 2x^{2} + 4x - \sqrt{2} \\
\end{align*}