(\partial)/(\partial y)(xe^{5xy})

解答

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

5 e^{5 x y} x^{2}

求解步骤

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

将

x

视为常数

将常数提出:

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

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

使用连锁律:

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

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

\frac{\partial}{\partial y} (5 x y) = 5 x

= x e^{5 x y} \cdot 5 x

化简

x e^{5 x y} \cdot 5 x : 5 e^{5 x y} x^{2}

= 5 e^{5 x y} x^{2}

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