(\partial)/(\partial x)((z)(x+y)e^y)

解答

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

e^{y} z

求解步骤

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

将

z, y

视为常数

将常数提出:

(a \cdot f)^{'} = a \cdot f^{'}

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

使用微分加减法定则:

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

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

\frac{\partial}{\partial x} (x) = 1

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

= z e^{y} (1 + 0)

化简

= e^{y} z

e x p an d (1 + 5)^{4}

e x p an d y (2 x - y + 1) d x - x (3 x - 4 y + 3) d y

s im pl i f y 6 (2 - 2 - 6 - 3)

e x p an d y (2 e^{2 x} y = \frac{x e ^{2 x}}{2} - \frac{e ^{2 x}}{4} + c)

e x p an d \frac{1}{4 - x}