微积分常用导数总结 - 清晰版 - 当然每一个都要熟记啦

$$\begin{array}{rl}& (C{)}^{\prime }=0\\ & (x^{\alpha }{)}^{\prime }=\alpha x^{\alpha -1}\\ & (\sin (x){)}^{\prime }=\cos (x)\\ & (\cos (x){)}^{\prime }=-\sin (x)\\ & (\tan (x){)}^{\prime }=\frac{1}{{\cos }^2(x)}={\sec }^2(x)\\ & (\cot (x){)}^{\prime }=-\frac{1}{{\sin }^2(x)}={\csc }^2(x)\\ & (\arcsin (x){)}^{\prime }=\frac{1}{\sqrt{1-x^2}}\\ & (\arccos (x){)}^{\prime }=-\frac{1}{\sqrt{1-x^2}}\\ & (\arctan (x){)}^{\prime }=\frac{1}{x^2+1}\\ & (\mathrm{a}\mathrm{r}\mathrm{c}\mathrm{c}\mathrm{o}\mathrm{t}(x){)}^{\prime }=-\frac{1}{1+x^2}\\ & (a^x{)}^{\prime }=\ln a\cdot a^x\\ & ({\log }_{a}x{)}^{\prime }=\frac{1}{\ln a}\cdot \frac{1}{x}\end{array}$$

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相关链接

常见函数泰勒公式展开
常用等价无穷小的整理

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2021年11月12日18:41:09