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Beliebt Rechnen >

derivative of (x^2+3x-9e^x)

Lösung

\frac{d}{d x} ((x^{2} + 3 x - 9) e^{x})

Lösung

e^{x} x^{2} + 5 e^{x} x - 6 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} + 3 x - 9) e^{x})

Wende die Produktregel an:

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

f = x^{2} + 3 x - 9, g = e^{x}

= \frac{d}{d x} (x^{2} + 3 x - 9) e^{x} + \frac{d}{d x} (e^{x}) (x^{2} + 3 x - 9)

\frac{d}{d x} (x^{2} + 3 x - 9) = 2 x + 3

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

= (2 x + 3) e^{x} + e^{x} (x^{2} + 3 x - 9)

Vereinfache

(2 x + 3) e^{x} + e^{x} (x^{2} + 3 x - 9) : e^{x} x^{2} + 5 e^{x} x - 6 e^{x}

= e^{x} x^{2} + 5 e^{x} x - 6 e^{x}

Graph

Beliebte Beispiele

derivative of x^3+ky(x^2-5xy)

\frac{d}{d x} (x^{3} + k y (x)^{2} - 5 x y)

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\int \frac{2 - x ^{2}}{x} d x

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