常用求导公式
$$(C)'=0$$
$$(x^a)' = ax^{a-1} a为实数$$
$$(a^x)' = a^x lna, (e^x)' = e^x$$
$$(log_ax)' = \frac{1}{xlna}, (ln|x|)' = \frac{1}{x}$$
$$(sinx)' = cosx$$
$$(cosx)' = -sinx$$
$$(tanx)' = \frac{1}{cos^2x}$$
$$(cotx)' = -\frac{1}{sin^2x}$$
$$(arcsinx)' = \frac{1}{\sqrt{1 - x^2}}$$
$$(arccosx)' = - \frac{1}{\sqrt{1 - x^2}}$$
$$(arctanx)' = \frac{1}{1 + x^2}$$
$$(\frac{e^x + e^{-x}}{2})' = \frac{e^x - e^{-x}}{2}$$
$$(\frac{e^x - e^{-x}}{2})' = \frac{e^x + e^{-x}}{2}$$
$$(ln(x + \sqrt{x^2 + 1}))' = \frac{1}{\sqrt{x^2 + 1}}$$
$$(ln(x + \sqrt{x^2 - 1}))' = \frac{1}{\sqrt{x^2 - 1}}$$