【微积分】入门

$$ \dfrac{\mathrm{d}f(x)}{\mathrm{d}x} = f'(x)$$

$$ \int f(x) \ \mathrm{d}x = F(x) + C$$

1. 初等函数

• $\mathrm{d}(C)=0$
• $\mathrm{d}(x^μ)=μx^{μ-1}\ \mathrm{d}x$
• $\mathrm{d}(\sin\ x)=\cos\ x\ \mathrm{d}x$
• $\mathrm{d}(\cos\ x)=-\sin\ x\ \mathrm{d}x$
• $\mathrm{d}(\tan\ x)=\dfrac{1}{\cos^2\ x}\ \mathrm{d}x$
• $\int x^n \ \mathrm{d}x = \dfrac{x^{n+1}}{n+1}+C$
• $\int \dfrac{1}{x} \ \mathrm{d}x = \ln|x|+C$
• $\int \cos \ x \ \mathrm{d}x = \sin \ x +C$
• $\int \sin \ x \ \mathrm{d}x = -\cos \ x + C$

2. 加减乘除

• $\mathrm{d}(u±v)=\mathrm{d}u±\mathrm{d}v$
• $\mathrm{d}(uv)=v\mathrm{d}u+u\mathrm{d}v$ --------> $\mathrm{d}(Cu)=C\mathrm{d}u$
• $\mathrm{d}(\dfrac{u}{v})=\dfrac{v\mathrm{d}u-u\mathrm{d}v}{v^2} (v \neq 0)$

3. 复合函数的链式法则

• $\dfrac{\mathrm{d}y}{\mathrm{d}x}=\dfrac{\mathrm{d}y}{\mathrm{d}u} \cdot \dfrac{\mathrm{d}u}{\mathrm{d}x}$

 

转载于:https://www.cnblogs.com/qixingzhi/p/10853747.html