(\partial)/(\partial x)(3xe^{5xy})

解答

\frac{\partial}{\partial x} (3 x e^{5 x y})

3 (e^{5 x y} + 5 e^{5 x y} x y)

求解步骤

\frac{\partial}{\partial x} (3 x e^{5 x y})

将

y

视为常数

将常数提出:

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

= 3 \frac{\partial}{\partial x} (x e^{5 x y})

使用微分乘法定则:

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

f = x, g = e^{5 x y}

= 3 (\frac{\partial}{\partial x} (x) e^{5 x y} + \frac{\partial}{\partial x} (e^{5 x y}) x)

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

\frac{\partial}{\partial x} (e^{5 x y}) = e^{5 x y} \cdot 5 y

= 3 (1 \cdot e^{5 x y} + e^{5 x y} \cdot 5 y x)

化简

= 3 (e^{5 x y} + 5 e^{5 x y} x y)

x \to - 4 lim (x)

\int \frac{x ^{2}}{( 1 + 2 x ) ^{\frac{1}{3}}} d x

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

\frac{\partial}{\partial r} (r^{2} + s^{2})

\frac{d}{d x} (sin (x))