derivative of ln(xe^{-7x})

Lösung

\frac{d}{d 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_{1.5}^{2.5} 9800 (7 - y) (1) d y

in v erse l a pl a ce \frac{1}{s ^{2} + 16}

in v erse l a pl a ce \frac{1}{s ( s ^{2} + s + \frac{5}{4} )}

d er i v a t i v e e^{x - 1}

\frac{\partial}{\partial x} (2 x y + 5 x^{2})