d/(dy)(x^{y^2})

解

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

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

解答ステップ

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

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

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

連鎖法則を適用:

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

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

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

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

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

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