derivative 1/(d+ke^d)

Lösung

ableitung von

\frac{1}{d + k e ^{d}}

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

Schritte zur Lösung

\frac{d}{dd} (\frac{1}{d + k e ^{d}})

Wende Exponentenregel an:

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

= \frac{d}{dd} ((d + k e^{d})^{- 1})

Wende die Kettenregel an:

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

= - \frac{1}{( d + k e ^{d} ) ^{2}} \frac{d}{dd} (d + k e^{d})

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

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

Vereinfache

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

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

\frac{d ^{2}}{d x ^{2}} y + 36 y = 0

\frac{\partial}{\partial x} (5 e^{x y})

\frac{d}{d x} (\frac{3 x - 5}{x ^{2} + 7})

\frac{d}{d x} (- 12 e^{- 2 x})

x \to 3 lim (\frac{3 x - 9}{x - 3})