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Beliebt Rechnen >

derivative of (e^x+e^{-x}/5)

Lösung

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{5})

Lösung

\frac{1}{5} (e^{x} - e^{- x})

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{x} + e ^{- x}}{5})

Entferne die Konstante:

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

= \frac{1}{5} \frac{d}{d x} (e^{x} + e^{- x})

Wende die Summen-/Differenzregel an:

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

= \frac{1}{5} (\frac{d}{d x} (e^{x}) + \frac{d}{d x} (e^{- x}))

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

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

= \frac{1}{5} (e^{x} - e^{- x})

Graph

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