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

解答

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

\frac{2 y}{x ^{3}} + 2 x y + 3 x

求解步骤

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

将

x

视为常数

使用微分加减法定则:

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

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

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

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

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

= \frac{2 y}{x ^{3}} + 2 x y + 3 x

n = 2 \sum \infty 5 (- \frac{3}{4})^{n}

d er i v a t i v e f (x) = 1 0^{x}

\int \frac{x ^{3} - 5 x ^{2} - x}{x ^{2}} d x

\int \frac{x}{144 x ^{2} - 1} d x

\int \frac{x}{x ^{2} - 4 x + 7} d x