derivative of ln((x^3/(e^{3x)}))

解

\frac{d}{d x} (ln (\frac{x ^{3}}{e ^{3 x}}))

\frac{3}{x} - 3

解答ステップ

\frac{d}{d x} (ln (\frac{x ^{3}}{e ^{3 x}}))

簡素化

ln (\frac{x ^{3}}{e ^{3 x}}) : ln (x^{3}) - 3 x

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

和/差の法則を適用:

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

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

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

\frac{d}{d x} (3 x) = 3

= \frac{3}{x} - 3