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人気のある微分積分 >

d/(dn)(n^n)

解

\frac{d}{d n} (n^{n})

解

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

解答ステップ

\frac{d}{d n} (n^{n})

指数の規則を適用する:

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

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

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

連鎖法則を適用:

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

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

\frac{d}{d n} (n ln (n)) = ln (n) + 1

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

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

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

グラフ

人気の例

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