(\partial)/(\partial z)(x^{yz})

解

\frac{\partial}{\partial z} (x^{yz})

y x^{yz} ln (x)

解答ステップ

\frac{\partial}{\partial z} (x^{yz})

x, y

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^{yz} = e^{yz l n (x)}

= \frac{\partial}{\partial z} (e^{yz l n (x)})

連鎖法則を適用:

e^{yz l n (x)} \frac{\partial}{\partial z} (yz ln (x))

= e^{yz l n (x)} \frac{\partial}{\partial z} (yz ln (x))

\frac{\partial}{\partial z} (yz ln (x)) = y ln (x)

= e^{yz l n (x)} y ln (x)

e^{yz l n (x)} = x^{yz}

= y x^{yz} ln (x)