derivative of cos((1-e^{9x}/(1+e^{9x)}))

Lösung

\frac{d}{d x} (cos (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}))

\frac{18 e ^{9 x} sin ( \frac{1 - e ^{9 x}}{1 + e ^{9 x}} )}{( 1 + e ^{9 x} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (cos (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}))

Wende die Kettenregel an:

- sin (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}) \frac{d}{d x} (\frac{1 - e ^{9 x}}{1 + e ^{9 x}})

= - sin (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}) \frac{d}{d x} (\frac{1 - e ^{9 x}}{1 + e ^{9 x}})

\frac{d}{d x} (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}) = - \frac{18 e ^{9 x}}{( 1 + e ^{9 x} ) ^{2}}

= - sin (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}) (- \frac{18 e ^{9 x}}{( 1 + e ^{9 x} ) ^{2}})

Vereinfache

- sin (\frac{1 - e ^{9 x}}{1 + e ^{9 x}}) (- \frac{18 e ^{9 x}}{( 1 + e ^{9 x} ) ^{2}}) : \frac{18 e ^{9 x} sin ( \frac{1 - e ^{9 x}}{1 + e ^{9 x}} )}{( 1 + e ^{9 x} ) ^{2}}

= \frac{18 e ^{9 x} sin ( \frac{1 - e ^{9 x}}{1 + e ^{9 x}} )}{( 1 + e ^{9 x} ) ^{2}}

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