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

解答

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

y

求解步骤

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

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

\frac{\partial}{\partial x} (2 y) = 0

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

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

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

= 0 + y + 0 - 0

化简

= y

\int \frac{5}{x ^{2} - 1} d x

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

x \to 2 lim (\frac{1}{x ^{2}})

x \to π lim (\frac{x}{3} - \frac{2 π}{3})

\frac{d ^{2} x}{d t ^{2}} + 4 x = t^{2}