derivative y=x^{x^2}

解

導関数

y = x^{x^{2}}

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

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

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

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