derivative of 1/12 (e^{6x}+e^{-6x})

Lösung

\frac{d}{d x} (\frac{1}{12} (e^{6 x} + e^{- 6 x}))

\frac{e ^{- 6 x} ( e ^{12 x} - 1 )}{2}

Schritte zur Lösung

\frac{d}{d x} (\frac{1}{12} (e^{6 x} + e^{- 6 x}))

Entferne die Konstante:

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

= \frac{1}{12} \frac{d}{d x} (e^{6 x} + e^{- 6 x})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= \frac{1}{12} (\frac{d}{d x} (e^{6 x}) + \frac{d}{d x} (e^{- 6 x}))

\frac{d}{d x} (e^{6 x}) = e^{6 x} \cdot 6

\frac{d}{d x} (e^{- 6 x}) = - 6 e^{- 6 x}

= \frac{1}{12} (e^{6 x} \cdot 6 - 6 e^{- 6 x})

Vereinfache

\frac{1}{12} (e^{6 x} \cdot 6 - 6 e^{- 6 x}) : \frac{e ^{- 6 x} ( e ^{12 x} - 1 )}{2}

= \frac{e ^{- 6 x} ( e ^{12 x} - 1 )}{2}

\int \frac{12}{( 1 + x + y ) ^{5}} d y

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