derivative of (x^2^x)

解

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

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

解答ステップ

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

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

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

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

簡素化

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

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