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

解答

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

e^{y} + e^{y} (x + y)

求解步骤

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

将

x

视为常数

使用微分乘法定则:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = x + y, g = e^{y}

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

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

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

= 1 \cdot e^{y} + e^{y} (x + y)

化简

= e^{y} + e^{y} (x + y)

x \frac{d y}{d x} - 3 y = x^{4}

\int_{1}^{e} ln (5 x^{3}) d x

\int_{0}^{5} (7 x - x^{2}) - 2 x d x

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

\int_{1}^{2} t^{4} f (t^{5}) d t