【Maths】导数和求导公式

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基本初等函数公式

1. C ′ = 0 C' = 0 C′=0 (C is constant)
2. ( x a ) ′ = a x a − 1 (x^a)' = ax^{a-1} (xa)′=axa−1, 多项式
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 (ax)′=ax⋅lna(a>0,a̸​=1);(ex)′=ex, 指数函数
4. ( log ⁡ a ∣ x ∣ ) ′ = 1 x ln ⁡ a , ( ln ⁡ ∣ x ∣ ) ′ = 1 x (\log_a\vert x \vert)' = \frac 1 {x\ln a}, (\ln\vert x \vert)' = \frac 1 x (loga​∣x∣)′=xlna1​,(ln∣x∣)′=x1​, 对数函数
5. ( sin ⁡ x ) ′ = cos ⁡ x (\sin x)' = \cos x (sinx)′=cosx
6. ( cos ⁡ x ) ′ = − sin ⁡ x (\cos x)' = -\sin x (cosx)′=−sinx

基本求导法则

1. 线性法则 ( a u + b v ) ′ = a u ′ + b v ′ (au+bv)' = au' + bv' (au+bv)′=au′+bv′
2. 积法则 $(uv)’ = u’v + uv’ $
3. 商法则 ( u v ) ′ = u ′ v − u v ′ v 2 (\frac u v)' = \frac {u'v - uv'}{v^2} (vu​)′=v2u′v−uv′​
4. 链式法则 ( f ( u ( x ) ) ) ′ = f ′ ( u ( x ) ) u ′ ( x ) (f(u(x)))' = f'(u(x))u'(x) (f(u(x)))′=f′(u(x))u′(x)

Ref

• 基本导数公式_百度文库