derivative of 2/(ln(10x^3))

解

\frac{d}{d x} (\frac{2}{ln ( 10 ) x ^{3}})

- \frac{6}{ln ( 10 ) x ^{4}}

解答ステップ

\frac{d}{d x} (\frac{2}{ln ( 10 ) x ^{3}})

定数を除去:

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

= \frac{2}{ln ( 10 )} \frac{d}{d x} (\frac{1}{x ^{3}})

指数の規則を適用する:

\frac{1}{a} = a^{- 1}

= \frac{2}{ln ( 10 )} \frac{d}{d x} (x^{- 3})

乗の法則を適用:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{2}{ln ( 10 )} (- 3 x^{- 3 - 1})

簡素化

\frac{2}{ln ( 10 )} (- 3 x^{- 3 - 1}) : - \frac{6}{ln ( 10 ) x ^{4}}

= - \frac{6}{ln ( 10 ) x ^{4}}