(\partial)/(\partial y)((x)(x^2y-xy^2))

解答

\frac{\partial}{\partial y} ((x) (x^{2} y - x y^{2}))

x (x^{2} - 2 x y)

求解步骤

\frac{\partial}{\partial y} ((x) (x^{2} y - x y^{2}))

将

x

视为常数

将常数提出:

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

= x \frac{\partial}{\partial y} (x^{2} y - x y^{2})

使用微分加减法定则:

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

= x (\frac{\partial}{\partial y} (x^{2} y) - \frac{\partial}{\partial y} (x y^{2}))

\frac{\partial}{\partial y} (x^{2} y) = x^{2}

\frac{\partial}{\partial y} (x y^{2}) = 2 x y

= x (x^{2} - 2 x y)

e x p an d (3 x y + 2 y) d x + 3 x d y

e x p an d F (- 3, - 3)

e x p an d b (- 3, 0) y f (0, - 4)

e x p an d \frac{14 ( n + 1 )}{n}

e x p an d \frac{2 x ^{3} - 24 x}{( x ^{2} + 4 ) ^{3}}