derivative of (2(axe^{-2x}+6))

解答

\frac{d}{d x} ((2) (a x e^{- 2 x} + 6))

2 a (- 2 e^{- 2 x} x + e^{- 2 x})

求解步骤

\frac{d}{d x} ((2) (a x e^{- 2 x} + 6))

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

= 2 \frac{d}{d x} (a x e^{- 2 x} + 6)

使用微分加减法定则:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 2 (\frac{d}{d x} (a x e^{- 2 x}) + \frac{d}{d x} (6))

\frac{d}{d x} (a x e^{- 2 x}) = a (e^{- 2 x} - 2 e^{- 2 x} x)

\frac{d}{d x} (6) = 0

= 2 (a (e^{- 2 x} - 2 e^{- 2 x} x) + 0)

化简

= 2 a (- 2 e^{- 2 x} x + e^{- 2 x})

e x p an d \frac{e ^{- s}}{s ^{3} ( s ^{2} + 1 )}

e x p an d (2 x - 5) \cdot e^{x}

e x p an d \frac{π ^{2} ( - 1 ) ^{n} n ^{2} - 2 ( - 1 ) ^{n} + 2}{n ^{3}}

e x p an d sin (θ) - cos (θ) (sin (θ) + cos (θ))

e x p an d (ln ∣ tan (x) + sec (x) ∣ - sin (x)) (sin (x))