derivative y=(200)/(0.9+0.1e^{2x)}

Lösung

ableitung von

y = \frac{200}{0.9 + 0.1 e ^{2 x}}

- \frac{40 e ^{2 x}}{( 0.9 + 0.1 e ^{2 x} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{200}{0.9 + 0.1 e ^{2 x}})

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 200 \frac{d}{d x} (\frac{1}{0.9 + 0.1 e ^{2 x}})

Wende Exponentenregel an:

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

= 200 \frac{d}{d x} ((0.9 + 0.1 e^{2 x})^{- 1})

Wende die Kettenregel an:

- \frac{1}{( 0.9 + 0.1 e ^{2 x} ) ^{2}} \frac{d}{d x} (0.9 + 0.1 e^{2 x})

= - \frac{1}{( 0.9 + 0.1 e ^{2 x} ) ^{2}} \frac{d}{d x} (0.9 + 0.1 e^{2 x})

\frac{d}{d x} (0.9 + 0.1 e^{2 x}) = 0.2 e^{2 x}

= 200 (- \frac{1}{( 0.9 + 0.1 e ^{2 x} ) ^{2}} \cdot 0.2 e^{2 x})

Vereinfache

200 (- \frac{1}{( 0.9 + 0.1 e ^{2 x} ) ^{2}} \cdot 0.2 e^{2 x}) : - \frac{40 e ^{2 x}}{( 0.9 + 0.1 e ^{2 x} ) ^{2}}

= - \frac{40 e ^{2 x}}{( 0.9 + 0.1 e ^{2 x} ) ^{2}}

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