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Beliebt Rechnen >

derivative of 10(1-e^{x/2})

Lösung

\frac{d}{d x} (10 (1 - e^{\frac{x}{2}}))

Lösung

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

Schritte zur Lösung

\frac{d}{d x} (10 (1 - e^{\frac{x}{2}}))

Entferne die Konstante:

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

= 10 \frac{d}{d x} (1 - e^{\frac{x}{2}})

Wende die Summen-/Differenzregel an:

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

= 10 (\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}}) = e^{\frac{x}{2}} \frac{1}{2}

= 10 (0 - e^{\frac{x}{2}} \frac{1}{2})

Vereinfache

10 (0 - e^{\frac{x}{2}} \frac{1}{2}) : - 5 e^{\frac{x}{2}}

= - 5 e^{\frac{x}{2}}

Graph

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