derivative of ln((e^x/x))

Lösung

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

1 - \frac{1}{x}

Schritte zur Lösung

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

Vereinfache

ln (\frac{e ^{x}}{x}) : x - ln (x)

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

Wende die Summen-/Differenzregel an:

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

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

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

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

= 1 - \frac{1}{x}

\frac{d}{d x} (5 x^{6})

s \to - 1 lim (\frac{1}{s ^{2} + 2 s + 1})

d er i v a t i v e (\frac{( x + 11 )}{( x - 11 )})^{5}

d er i v a t i v e y = x - 1

\int \frac{4}{15} t^{\frac{5}{2}} + 3 cos (t) + Ct + C d t