Standard results

$$\begin{eqnarray*} y = x^{n} & \Rightarrow & \frac{\mathrm{d}y}{\mathrm{d}x} = n ... ...} & \Rightarrow & \frac{\mathrm{d}y}{\mathrm{d}x} = -\sin{x} \\ \end{eqnarray*}$$

This is only a very small number of results, but it will be sufficient for our purposes.