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

解答

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

x (y^{2} - 1)

求解步骤

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

将

x

视为常数

将常数提出:

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

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

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} (\frac{y ^{3}}{3}) - \frac{d y}{d y})

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

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

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

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

化简

= x (y^{2} - 1)

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

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

e x p an d a (3, - 1) b (3, 7)

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

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