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人気のある微分積分 >

(x^x)^'

解

(x^{x})^{^{'}}

解

x^{x} (ln (x) + 1)

解答ステップ

(x^{x})^{'}

指数の規則を適用する:

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

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

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

連鎖法則を適用:

e^{x l n (x)} (x ln (x))^{'}

= e^{x l n (x)} (x ln (x))^{'}

(x ln (x))^{'} = ln (x) + 1

= e^{x l n (x)} (ln (x) + 1)

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

= x^{x} (ln (x) + 1)

グラフ

人気の例

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