(\partial)/(\partial x)(3xy-x^2y^2+23)

解答

\frac{\partial}{\partial x} (3 x y - x^{2} y^{2} + 23)

- 2 x y^{2} + 3 y

求解步骤

\frac{\partial}{\partial x} (3 x y - x^{2} y^{2} + 23)

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} (3 x y) - \frac{\partial}{\partial x} (x^{2} y^{2}) + \frac{\partial}{\partial x} (23)

\frac{\partial}{\partial x} (3 x y) = 3 y

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

\frac{\partial}{\partial x} (23) = 0

= 3 y - 2 y^{2} x + 0

化简

= - 2 x y^{2} + 3 y

\frac{d y}{d x} = \frac{x}{e ^{y}}

d er i v a t i v e 3 x^{2} - 2

d er i v a t i v e f (x) = - 9.8 x^{2} + 2 x + 1

\int \frac{1}{arcsin ( x ) 1 - x ^{2}} d x

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