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Beliebt Rechnen >

derivative of ln(3xe^{-x})

Lösung

\frac{d}{d 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

Beliebte Beispiele

fläche 15-x^2,-6x-1,[-4,-1]

a re a 15 - x^{2}, - 6 x - 1, [- 4, - 1]

integral of 9/((x+1)^2)

\int \frac{9}{( x + 1 ) ^{2}} d x

integral of (1-2x)/((x+1)(x-5))

\int \frac{1 - 2 x}{( x + 1 ) ( x - 5 )} d x

derivative of xe^{xy}+2xy+1/x

\frac{d}{d x} (x e^{x y} + 2 x y + \frac{1}{x})

y^'-e^y-2xe^y=0

y^{^{'}} - e^{y} - 2 x e^{y} = 0