derivative of ln((7+e^x/(7-e^x)))

Lösung

\frac{d}{d x} (ln (\frac{7 + e ^{x}}{7 - e ^{x}}))

\frac{14 e ^{x}}{( e ^{x} + 7 ) ( - e ^{x} + 7 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{7 + e ^{x}}{7 - e ^{x}}))

Wende die Kettenregel an:

\frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \frac{d}{d x} (\frac{7 + e ^{x}}{7 - e ^{x}})

= \frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \frac{d}{d x} (\frac{7 + e ^{x}}{7 - e ^{x}})

\frac{d}{d x} (\frac{7 + e ^{x}}{7 - e ^{x}}) = \frac{14 e ^{x}}{( 7 - e ^{x} ) ^{2}}

= \frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \cdot \frac{14 e ^{x}}{( 7 - e ^{x} ) ^{2}}

Vereinfache

\frac{1}{\frac{7 + e ^{x}}{7 - e ^{x}}} \cdot \frac{14 e ^{x}}{( 7 - e ^{x} ) ^{2}} : \frac{14 e ^{x}}{( e ^{x} + 7 ) ( - e ^{x} + 7 )}

= \frac{14 e ^{x}}{( e ^{x} + 7 ) ( - e ^{x} + 7 )}

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