(\partial)/(\partial y)(x^{8y})

解

\frac{\partial}{\partial y} (x^{8 y})

8 x^{8 y} ln (x)

解答ステップ

\frac{\partial}{\partial y} (x^{8 y})

x

を定数として扱う

指数の規則を適用する:

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

x^{8 y} = e^{8 y l n (x)}

= \frac{\partial}{\partial y} (e^{8 y l n (x)})

連鎖法則を適用:

e^{8 y l n (x)} \frac{\partial}{\partial y} (8 y ln (x))

= e^{8 y l n (x)} \frac{\partial}{\partial y} (8 y ln (x))

\frac{\partial}{\partial y} (8 y ln (x)) = 8 ln (x)

= e^{8 y l n (x)} \cdot 8 ln (x)

e^{8 y l n (x)} = x^{8 y}

= 8 x^{8 y} ln (x)