常见
\((x^n)' = nx^{n-1}\)
\((sin(x))' = cos(x)\)
\((cos(x))' = -sin(x)\)
\((x^n)' = nx^{n-1}\)
\(n \in Z^+\)
\(\lim_{\Delta x \to 0} \frac{(x+\Delta x)^n - x^n}{\Delta x} = \lim_{\Delta x \to 0} \frac{nx^{n-1}\Delta x+O(\Delta x^2)}{\Delta x} = \lim_{\Delta x \to 0}{nx^{n-1}+O(\Delta x)} = nx^{n-1}\)（二项式定理）
\(n \in Z\)
\(n < 0,(x^n)' = (\frac{1}{x^{-n}})' = \frac{nx^{-n-1}}{x^{-2n}} = nx^{n-1}\)（除法求导法则）
\(n \in Q\)
\(y = x^n = x^{\frac{a}{b}}\)，\(y^{b} = x^a\)
\(by^{b-1}y'=ax^{a-1}\)（隐式求导法则）
\(y' = \frac{a}{b}x^{\frac{a}{b}-1} = nx^{{n-1}}\)
\((e^x)' = e^x\)
标签：cos,frac,lim,微积分,笔记,nx,Delta,求导 From： https://www.cnblogs.com/J-12045/p/18554041