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Beliebt Rechnen >

derivative of 6x^2e^{-x}

Lösung

\frac{d}{d x} (6 x^{2} e^{- x})

Lösung

6 (2 e^{- x} x - e^{- x} x^{2})

Schritte zur Lösung

\frac{d}{d x} (6 x^{2} e^{- x})

Entferne die Konstante:

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

= 6 \frac{d}{d x} (x^{2} e^{- x})

Wende die Produktregel an:

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

f = x^{2}, g = e^{- x}

= 6 (\frac{d}{d x} (x^{2}) e^{- x} + \frac{d}{d x} (e^{- x}) x^{2})

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

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

= 6 (2 x e^{- x} + (- e^{- x}) x^{2})

Vereinfache

= 6 (2 e^{- x} x - e^{- x} x^{2})

Graph

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derivative of-x^3+5x^2-6x

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