\begin{eqnarray} d(a) &=& 0\\ d(u^n) &=& nu^{n-1}du\\ d(uv) &=& udv + vdu\\ d(e^u) &=& e^udu\\ d(sinu) &=& cosu du\\ d(cosu) &=& -sinudu\\ d(lnu) &=& \frac{1}{u}du\\ \end{eqnarray}