内容纲要
- $$c\prime = 0 \quad （c为常数）$$
- $$(\it e^x)\prime = \it e^x$$
- $$(x^a)\prime = ax^{a-1}$$
- $$(a^x)\prime = a^x\ln a \quad （a\gt0,a\neq1）$$
- $$(\log _a x)\prime = \frac{1}{x\ln a} \quad （a\gt0,a\neq1）$$
- $$(\ln x)\prime = \frac{1}{x} \quad （ln为自然对数）$$
- $$(\sin x)\prime = \cos x$$
- $$(\tan x)\prime = \frac{1}{\cos^2 x} = \sec^2x$$
- $$(\cos x)\prime = -\sin x$$
- $$(\cot x)\prime = -\frac{1}{\sin^2x} = -\csc^2x$$
- $$(\arcsin x)\prime = \frac{1}{\sqrt{1-x^2}}$$
- $$(\arctan x)\prime = \frac{1}{1+x^2}$$
- $$(\arccos x)\prime = \frac{-1}{\sqrt{1-x^2}}$$
- $$(\rm arccot \ \it x)\prime = \frac{-1}{1+x^2}$$
- $$(\csc x)\prime = -\csc x*\cot x$$
- $$(\sec x)\prime = \sec x*\tan x$$
- $$(\sinh x)\prime = \cosh x \quad（双曲函数）$$