(\partial)/(\partial y)(x^{2y})

解答

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

2 x^{2 y} ln (x)

求解步骤

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

将

x

视为常数

使用指数法则:

a^{b} = e^{b l n (a)}

x^{2 y} = e^{2 y l n (x)}

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

使用连锁律:

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

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

\frac{\partial}{\partial y} (2 y ln (x)) = 2 ln (x)

= e^{2 y l n (x)} \cdot 2 ln (x)

e^{2 y l n (x)} = x^{2 y}

= 2 x^{2 y} ln (x)

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