derivative of (e^x+e^{-x}/2)

Lösung

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

y^{^{''}} - 10 y^{^{'}} + 25 y = 0, y (0) = - 3, y^{^{'}} (0) = - \frac{29}{2}

d er i v a t i v e f (x) = - \frac{13}{x ^{4}}

\int \frac{( 2 x + 3 )}{( x + 1 ) ^{2}} d x

t an g e n t 110 x - 16 x^{2}

\frac{d}{d x} (16)