derivative of log_{3}(xe^x)

解

\frac{d}{d x} (lo g_{3} (x e^{x}))

\frac{1}{x ln ( 3 )} + lo g_{3} (e)

解答ステップ

\frac{d}{d x} (lo g_{3} (x e^{x}))

簡素化

lo g_{3} (x e^{x}) : lo g_{3} (x) + lo g_{3} (e) x

= \frac{d}{d x} (lo g_{3} (x) + lo g_{3} (e) x)

和/差の法則を適用:

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

= \frac{d}{d x} (lo g_{3} (x)) + \frac{d}{d x} (lo g_{3} (e) x)

\frac{d}{d x} (lo g_{3} (x)) = \frac{1}{x ln ( 3 )}

\frac{d}{d x} (lo g_{3} (e) x) = lo g_{3} (e)

= \frac{1}{x ln ( 3 )} + lo g_{3} (e)