幂指函数

其中 $a$, $c$, $n$ 都是常数：

$$\frac{d}{dx} (c) = 0$$

$$\frac{d}{dx} (x^n) = nx^{n-1}$$

$$\frac{d}{dx} (a^x) = a^x \ln(a),(a > 0)$$

$$\frac{d}{dx} (\log_a x) = \frac{1}{x \ln(a)},其中(a > 0, a \neq 1)$$

三角函数

$$\frac{d}{dx}(\sin(x)) = \cos(x)$$

$$\frac{d}{dx}(\cos(x)) = -\sin(x)$$

$$\frac{d}{dx}(\tan(x)) = \sec^2(x)$$

$$\frac{d}{dx}(\cot(x)) = -\csc^2(x)$$

$$\frac{d}{dx}(\sec(x)) = \sec(x) \tan(x)$$

$$\frac{d}{dx}(\csc(x)) = -\csc(x) \cot(x)$$

反三角函数

$$\frac{d}{dx}(\arcsin(x)) = \frac{1}{\sqrt{1-x^2}}$$

$$\frac{d}{dx}(\arccos(x)) = -\frac{1}{\sqrt{1-x^2}}$$

$$\frac{d}{dx}(\arctan(x)) = \frac{1}{1+x^2}$$

$$\frac{d}{dx}(arccot(x)) = -\frac{1}{1+x^2}$$

$$\frac{d}{dx}(arcsec(x)) = \frac{1}{|x|\sqrt{x^2-1}}$$

$$\frac{d}{dx}(arccsc(x)) = -\frac{1}{|x|\sqrt{x^2-1}}$$

导数间的运算法则

线性乘法定则除法定则链式法则