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基本初等函式公式

1. $C' = 0$ (C is constant)
2. $(x^a{)}^{\mathrm{\prime }}=a$
   x a − 1 (x^a)' = ax^{a-1} , 多項式
3. $($
   a x ) ′ = a x ⋅ ln ⁡ a ( a > 0 , a ≠ 1 ) ; ( e x ) ′ = e x (a^x)' = a^x\cdot \ln a(a>0, a \neq 1); (e^x)' = e^x , 指數函式
4. $(\log_a\vert x \vert)' = \frac 1 {x\ln a}, (\ln\vert x \vert)' = \frac 1 x$, 對數函式
5. $(\sin x)' = \cos x$
6. $(\cos x)' = -\sin x$

基本求導法則

1. 線性法則 $(au+bv)' = au' + bv'$
2. 積法則 $(uv)’ = u’v + uv’ $
3. 商法則 $(\frac u v)' = \frac {u'v - uv'}{v^2}$
4. 鏈式法則 $(f(u(x)))' = f'(u(x))u'(x)$

Ref

• 基本導數公式_百度文庫