d/(dy)((x)(x^2+y^2+y-2x-y^3))

解答

\frac{d}{d y} ((x) (x^{2} + y^{2} + y - 2 x - y^{3}))

x (- 3 y^{2} + 2 y + 1)

求解步骤

\frac{d}{d y} ((x) (x^{2} + y^{2} + y - 2 x - y^{3}))

将

x

视为常数

将常数提出:

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

= x \frac{d}{d y} (x^{2} + y^{2} + y - 2 x - y^{3})

使用微分加减法定则:

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

= x (\frac{d}{d y} (x^{2}) + \frac{d}{d y} (y^{2}) + \frac{d y}{d y} - \frac{d}{d y} (2 x) - \frac{d}{d y} (y^{3}))

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

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

\frac{d y}{d y} = 1

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

\frac{d}{d y} (y^{3}) = 3 y^{2}

= x (0 + 2 y + 1 - 0 - 3 y^{2})

化简

= x (- 3 y^{2} + 2 y + 1)

\frac{d}{d x} ((f (x)) (9 x^{2} + 11 x + 2))

e x p an d (4 + 32) (- 3 + 5)

e x p an d (8 x^{2} - 16 x + 16) e^{x}

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

e x p an d (4 x - 8) (2 x + 3)