derivative of-(x^{ln(x})/6)

解

\frac{d}{d x} (- \frac{x ^{l n (x)}}{6})

- \frac{e ^{l n^{2} (x)} ln ( x )}{3 x}

解答ステップ

\frac{d}{d x} (- \frac{x ^{l n (x)}}{6})

定数を除去:

(a \cdot f)^{'} = a \cdot f^{'}

= - \frac{1}{6} \frac{d}{d x} (x^{l n (x)})

指数の規則を適用する:

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

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

= - \frac{1}{6} \frac{d}{d x} (e^{l n (x) l n (x)})

連鎖法則を適用:

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

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

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

= - \frac{1}{6} e^{l n (x) l n (x)} \frac{2 ln ( x )}{x}

簡素化

- \frac{1}{6} e^{l n (x) l n (x)} \frac{2 ln ( x )}{x} : - \frac{e ^{l n^{2} (x)} ln ( x )}{3 x}

= - \frac{e ^{l n^{2} (x)} ln ( x )}{3 x}