derivative g(x)=ln(xe^{-7x})

Lösung

ableitung von

g (x) = ln (x e^{- 7 x})

\frac{1}{x} - 7

Schritte zur Lösung

\frac{d}{d x} (ln (x e^{- 7 x}))

Vereinfache

ln (x e^{- 7 x}) : ln (x) - 7 x

= \frac{d}{d x} (ln (x) - 7 x)

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (ln (x)) - \frac{d}{d x} (7 x)

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

\frac{d}{d x} (7 x) = 7

= \frac{1}{x} - 7

\int \frac{u}{u ^{2} + 1} d u

x \to 0 lim (\frac{ln ( \frac{1 + x}{1 - x} ) - 2 x}{x - sin ( x )})

d er i v a t i v e f (t) = 80 t + t^{2} - \frac{1}{48} t^{3}

\int_{1}^{16} \frac{8}{x} d x

d er i v a t i v e f (x) = e^{- 4 x}