(\partial)/(\partial u)(5u^2v^3+2u^2+7v)

解答

\frac{\partial}{\partial u} (5 u^{2} v^{3} + 2 u^{2} + 7 v)

10 u v^{3} + 4 u

求解步骤

\frac{\partial}{\partial u} (5 u^{2} v^{3} + 2 u^{2} + 7 v)

将

v

视为常数

使用微分加减法定则:

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

= \frac{\partial}{\partial u} (5 u^{2} v^{3}) + \frac{\partial}{\partial u} (2 u^{2}) + \frac{\partial}{\partial u} (7 v)

\frac{\partial}{\partial u} (5 u^{2} v^{3}) = 10 v^{3} u

\frac{\partial}{\partial u} (2 u^{2}) = 4 u

\frac{\partial}{\partial u} (7 v) = 0

= 10 v^{3} u + 4 u + 0

化简

= 10 u v^{3} + 4 u

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

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

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

a re a x + 8, x = 0, y = 0

d er i v a t i v e y = \frac{x + x ^{2}}{e ^{x} + 1}