(\partial)/(\partial x)(z^{xy^2})

解

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

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

解答ステップ

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

z, 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)}

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

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

連鎖法則を適用:

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

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

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

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

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

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