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Beliebt Rechnen >

derivative of 1000(sin(x)(e^{-2x}))

Lösung

\frac{d}{d x} (1000 (sin (x)) (e^{- 2 x}))

Lösung

1000 (e^{- 2 x} cos (x) - 2 e^{- 2 x} sin (x))

Schritte zur Lösung

\frac{d}{d x} (1000 (sin (x)) (e^{- 2 x}))

Entferne die Konstante:

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

= 1000 \frac{d}{d x} (sin (x) e^{- 2 x})

Wende die Produktregel an:

(f \cdot g)^{'} = f^{'} \cdot g + f \cdot g^{'}

f = sin (x), g = e^{- 2 x}

= 1000 (\frac{d}{d x} (sin (x)) e^{- 2 x} + \frac{d}{d x} (e^{- 2 x}) sin (x))

\frac{d}{d x} (sin (x)) = cos (x)

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

= 1000 (cos (x) e^{- 2 x} + (- 2 e^{- 2 x}) sin (x))

Vereinfache

= 1000 (e^{- 2 x} cos (x) - 2 e^{- 2 x} sin (x))

Graph

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