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Beliebt Rechnen >

derivative f(x)=ln(3xe^{-x})

Lösung

ableitung von

f (x) = ln (3 x e^{- x})

Lösung

\frac{1}{x} - 1

Schritte zur Lösung

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

Vereinfache

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

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

Wende die Summen-/Differenzregel an:

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

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

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

\frac{d x}{d x} = 1

= \frac{1}{x} - 1

Graph

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