d/(dy)((x)(xy+2y-x-2))

解答

\frac{d}{d y} ((x) (x y + 2 y - x - 2))

x (x + 2)

求解步骤

\frac{d}{d y} ((x) (x y + 2 y - x - 2))

将

x

视为常数

将常数提出:

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

= x \frac{d}{d y} (x y + 2 y - x - 2)

使用微分加减法定则:

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

= x (\frac{d}{d y} (x y) + \frac{d}{d y} (2 y) - \frac{d x}{d y} - \frac{d}{d y} (2))

\frac{d}{d y} (x y) = x

\frac{d}{d y} (2 y) = 2

\frac{d x}{d y} = 0

\frac{d}{d y} (2) = 0

= x (x + 2 - 0 - 0)

化简

= x (x + 2)

e x p an d \frac{12}{- 8}

e x p an d - 1 (- 3 x^{2} + 2 x - 5 = 0)

e x p an d (t e^{t y} cos (2 t) - 3) d t

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

e x p an d \frac{1}{x ^{2} ( x ^{2} - 4 ) ^{2}}