d/(dy)((x)(e^{-3x}-(3y+1)x))

解答

\frac{d}{d y} ((x) (e^{- 3 x} - (3 y + 1) x))

- 3 x^{2}

求解步骤

\frac{d}{d y} ((x) (e^{- 3 x} - (3 y + 1) x))

将

x

视为常数

将常数提出:

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

= x \frac{d}{d y} (e^{- 3 x} - (3 y + 1) x)

使用微分加减法定则:

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

= x (\frac{d}{d y} (e^{- 3 x}) - \frac{d}{d y} ((3 y + 1) x))

\frac{d}{d y} (e^{- 3 x}) = 0

\frac{d}{d y} ((3 y + 1) x) = 3 x

= x (0 - 3 x)

化简

x (0 - 3 x) : - 3 x^{2}

= - 3 x^{2}

e x p an d (x - \frac{3}{2}) (x - \frac{3}{2})

e x p an d 3 (7 + 6)

s im pl i f y 3 (3 + 2)

e x p an d \frac{2 ( X + 1 )}{3}

e x p an d \frac{152 ( - 3 t ^{2} + 4 )}{( 4 + t ^{2} ) ^{3}}