(\partial)/(\partial x)(2x*e^{xy})

解答

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

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

求解步骤

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

将

y

视为常数

将常数提出:

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

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

使用微分乘法定则:

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

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

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

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

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

= 2 (1 \cdot e^{x y} + e^{x y} y x)

化简

= 2 (e^{x y} + e^{x y} x y)

\frac{\partial}{\partial x} (x^{2} z + 3 z^{2} x + 6 (x + z))

\frac{d}{d x} (2 x^{6} - 8 x^{5} + 10 x^{4} - 10 x^{2} + 8 x - 2)

\int \frac{x - 4}{x ^{2} + 2 x - 15} d x

\int_{0}^{1} \frac{x}{1 + x ^{4}} d x

a re a y = 3 x, [3, 7]