derivative 1/(m+ke^m)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende Exponentenregel an:

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

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

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