(\partial)/(\partial x)(x^2y-3y^4)

解答

\frac{\partial}{\partial x} (x^{2} y - 3 y^{4})

2 x y

求解步骤

\frac{\partial}{\partial x} (x^{2} y - 3 y^{4})

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^{2} y) - \frac{\partial}{\partial x} (3 y^{4})

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

\frac{\partial}{\partial x} (3 y^{4}) = 0

= 2 y x - 0

化简

= 2 x y

\frac{d}{d x} (\frac{1}{5} (x y^{2} + 4 y)^{2})

f (x) = \frac{1}{2 x ^{3}}

\frac{d}{d x} (ln (\frac{x}{x ^{2} + 5}))

\int - \frac{2}{t + 1} d t

9 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = 2