derivative ln(xe^{-4x})

Lösung

ableitung von

ln (x e^{- 4 x})

\frac{1}{x} - 4

Schritte zur Lösung

\frac{d}{d x} (ln (x e^{- 4 x}))

Vereinfache

ln (x e^{- 4 x}) : ln (x) - 4 x

= \frac{d}{d x} (ln (x) - 4 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (4 x)

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

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

= \frac{1}{x} - 4

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