(\partial)/(\partial x)(bxe^{2xy})

解答

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

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

求解步骤

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

将

b, y

视为常数

将常数提出:

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

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

使用微分乘法定则:

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

f = x, g = e^{2 x y}

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

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

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

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

化简

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

\int 4 x^{2} + 9 x^{4} d x

\frac{d}{d x} (1 0^{n x})

d er i v a t i v e f (x) = \frac{14}{( x + 4 ) ^{3}}

\frac{d y}{d x} = \frac{cos ( x )}{y}

n = 1 \sum \infty \frac{5 n}{2 n - 1}