(\partial)/(\partial y)(9x^{8y})

解

\frac{\partial}{\partial y} (9 x^{8 y})

72 x^{8 y} ln (x)

解答ステップ

\frac{\partial}{\partial y} (9 x^{8 y})

x

を定数として扱う

定数を除去:

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

= 9 \frac{\partial}{\partial y} (x^{8 y})

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)}

= 9 \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)

= 9 e^{8 y l n (x)} \cdot 8 ln (x)

簡素化

9 e^{8 y l n (x)} \cdot 8 ln (x) : 72 x^{8 y} ln (x)

= 72 x^{8 y} ln (x)