\begin{align}
&C' = 0
\\
&(x^n)' = nx^{n-1}
\\
&(sinx)' = cosx
\\
&(cosx)' = -sinx
\\
&(a^x)' = a^xlna
\\
&(e^x)' = e^x
\\
&(log_ax)' = \frac1xlog_ae
\\
&(lnx)' = \frac1x
\\
&(u + v)' = u' + v'
\\
&(uv)' = u'v + uv'
\end{align}
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