02 常见函数的导数

高频率求导函数：

$\{\begin{array}{l}(x^a{)}^{\prime }=a{x}^{a-1}\\ (c{)}^{\prime }=0\\ (e^x{)}^{\prime }=e^x\\ (lnx{)}^{\prime }=\frac{1}{x}\\ (sinx{)}^{\prime }=cosx\\ (cosx{)}^{\prime }=-sinx\end{array}$

低频率求导函数：

$\{\begin{array}{l}(tanx{)}^{\prime }=\frac{1}{co{s}^{2}x}\\ (cotx{)}^{\prime }=(\frac{1}{tanx}{)}^{\prime }=-\frac{1}{si{n}^{2}x}\\ (a^x{)}^{\prime }=a^{x}lna\\ (lo{g}_{a}x{)}^{\prime }=\frac{1}{xlna}\end{array}$

例子

$(\sqrt{x}{)}^{\prime }=\frac{1}{2}{x}^{-\frac{1}{2}}$

$y=x^{-\frac{1}{2}}+e^x+3lnx-sinx+cosx+4x^7+18$

$y^{\prime }=-\frac{1}{2}\cdot 1{\sqrt{x}}^3+e^x+\frac{3}{x}-cosx-sinx+28x^6$