derivative of 5ln(x^5)

解

\frac{d}{d x} (5 ln (x^{5}))

\frac{25}{x}

解答ステップ

\frac{d}{d x} (5 ln (x^{5}))

定数を除去:

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

= 5 \frac{d}{d x} (ln (x^{5}))

連鎖法則を適用:

\frac{1}{x ^{5}} \frac{d}{d x} (x^{5})

= \frac{1}{x ^{5}} \frac{d}{d x} (x^{5})

\frac{d}{d x} (x^{5}) = 5 x^{4}

= 5 \cdot \frac{1}{x ^{5}} \cdot 5 x^{4}

簡素化

5 \cdot \frac{1}{x ^{5}} \cdot 5 x^{4} : \frac{25}{x}

= \frac{25}{x}