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Beliebt Rechnen >

derivative 3(e^xcos(x)-e^xsin(x))

Lösung

ableitung von

3 (e^{x} cos (x) - e^{x} sin (x))

Lösung

- 6 e^{x} sin (x)

Schritte zur Lösung

\frac{d}{d x} (3 (e^{x} cos (x) - e^{x} sin (x)))

Entferne die Konstante:

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

= 3 \frac{d}{d x} (e^{x} cos (x) - e^{x} sin (x))

Wende die Summen-/Differenzregel an:

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

= 3 (\frac{d}{d x} (e^{x} cos (x)) - \frac{d}{d x} (e^{x} sin (x)))

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

\frac{d}{d x} (e^{x} sin (x)) = e^{x} sin (x) + cos (x) e^{x}

= 3 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x}))

Vereinfache

3 (e^{x} cos (x) - e^{x} sin (x) - (e^{x} sin (x) + cos (x) e^{x})) : - 6 e^{x} sin (x)

= - 6 e^{x} sin (x)

Graph

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