derivative of 1/(sqrt(e^x))

Lösung

\frac{d}{d x} (\frac{1}{e ^{x}})

- \frac{1}{2 e ^{\frac{x}{2}}}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{e ^{x}})

Wende Exponentenregel an:

\frac{1}{a} = a^{- 1}

= \frac{d}{d x} ((e^{x})^{- \frac{1}{2}})

Wende die Kettenregel an:

- \frac{1}{2 ( e ^{x} ) ^{\frac{3}{2}}} \frac{d}{d x} (e^{x})

= - \frac{1}{2 ( e ^{x} ) ^{\frac{3}{2}}} \frac{d}{d x} (e^{x})

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

= - \frac{1}{2 ( e ^{x} ) ^{\frac{3}{2}}} e^{x}

Vereinfache

- \frac{1}{2 ( e ^{x} ) ^{\frac{3}{2}}} e^{x} : - \frac{1}{2 e ^{\frac{x}{2}}}

= - \frac{1}{2 e ^{\frac{x}{2}}}

l a pl a ce t r an s f or m t^{3} δ (t - 1)

x \to 8 lim (2 x - 1)

\frac{d}{d x} (cos (14 x))

\frac{d}{d x} (\frac{ln ( x ^{2} )}{e ^{2 x}})

n = 0 \sum \infty \frac{1}{n ^{2} + 3 n + 2}