常用高阶导数公式

$n$ 为正整数：

$$(e^{ax+b}{)}^{(n)}=a^n{e}^{ax+b}$$

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$$[\sin (ax+b){]}^{(n)}=a^n\sin \left(ax+b+\frac{n\pi }{2}\right)$$ $$[\cos (ax+b){]}^{(n)}=a^n\cos \left(ax+b+\frac{n\pi }{2}\right)$$

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$$[\ln (ax+b){]}^{(n)}=(-1{)}^{n-1}{a}^n\frac{(n-1)!}{(ax+b{)}^n}$$ $${\left(\frac{1}{ax+b}\right)}^{(n)}=(-1{)}^n{a}^n\frac{n!}{(ax+b{)}^{n+1}}$$