derivative of (1+e^x^{-2})

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Multipliziere Brüche:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

\frac{d}{d x} (x^{3} + 10 x^{2} + 25 x)

\int_{0}^{1} \frac{x}{4 - x ^{2}} d x

\frac{d ^{2} y}{d x ^{2}} + 2 \frac{d y}{d x} + 5 y = 0

\frac{d}{d x} (\frac{sin ^{2} ( x )}{cos ^{2} ( x )})

\int x^{a} d x