导数
\[f'(x)=\frac{f(x+\Delta x)-f(x)}{\Delta x} \]有用的导数基本公式：
\[\begin{aligned} f(x)=e^x&\implies f'(x)=e^x\\ f(x)=a&\implies f'(x)=0\\ f(x)=\ln a&\implies f'(x)=\frac{1}{x}\\ f(x)=ax^t&\implies f'(x)=atx^{t-1}\\ (f(x)+g(x))'&\implies f'(x)+g'(x)\\ (f(g(x)))'&\implies f'(g(x))\times g'(x) \end{aligned} \]\[f(x)=\sum_{i=0}^n a_ix^i\implies f'(x)=\sum_{i=0}^{n-1}(i+1)a_{i+1}x^i \]积分
多项式 \(f(x)=\sum_{i=0}^na_ix^i\) 积分：
\[\sum_{i=1}^{n+1} \frac{a_{i-1}x^i}{i} \] 标签：ix,frac,导数,积分,sum,implies From： https://www.cnblogs.com/dadidididi/p/17692281.html