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

解答

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

y^{2} - 2 x y + 1

求解步骤

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

将

y

视为常数

使用微分加减法定则:

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

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

\frac{\partial}{\partial x} (x) = 1

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

\frac{\partial}{\partial x} (y) = 0

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

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

化简

= y^{2} - 2 x y + 1

x \to 0 lim (x^{7} sin (\frac{1}{x}))

d er i v a t i v e (9 - \frac{x}{9})^{- 7}

a re a x = - 2, x = 1, y = 7 x, y = x^{2} - 8

im pl i c i t \frac{d y}{d x}, 6 x^{2} + 3 x y + 2 y^{2} + 17 y - 6 = 0

y^{^{''}} - 7 y^{^{'}} + 12 y = 0