derivative-10ln(xe^{x^8})

解

導関数

- 10 ln (x e^{x^{8}})

- 10 (\frac{1}{x} + 8 x^{7})

解答ステップ

\frac{d}{d x} (- 10 ln (x e^{x^{8}}))

簡素化

- 10 ln (x e^{x^{8}}) : - 10 (ln (x) + x^{8})

= \frac{d}{d x} (- 10 (ln (x) + x^{8}))

定数を除去:

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

= - 10 \frac{d}{d x} (ln (x) + x^{8})

和/差の法則を適用:

(f \pm g)^{'} = f^{'} \pm g^{'}

= - 10 (\frac{d}{d x} (ln (x)) + \frac{d}{d x} (x^{8}))

\frac{d}{d x} (ln (x)) = \frac{1}{x}

\frac{d}{d x} (x^{8}) = 8 x^{7}

= - 10 (\frac{1}{x} + 8 x^{7})