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Beliebt Rechnen >

derivative of 1-e^{-x/2}

Lösung

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

Lösung

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

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (1) = 0

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

= 0 - (- \frac{1}{2} e^{- \frac{x}{2}})

Vereinfache

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

Graph

Beliebte Beispiele

steigung 1/(x-5)

s l o p e \frac{1}{x - 5}

derivative of (3x+2^3)

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

integral from 0 to 1 of 5ln(x)

\int_{0}^{1} 5 ln (x) d x

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integral from 1 to e of 1/(x(x^2+1))

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