derivative (6x^2-9x)e^x

Lösung

ableitung von

(6 x^{2} - 9 x) e^{x}

6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((6 x^{2} - 9 x) e^{x})

Wende die Produktregel an:

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

f = 6 x^{2} - 9 x, g = e^{x}

= \frac{d}{d x} (6 x^{2} - 9 x) e^{x} + \frac{d}{d x} (e^{x}) (6 x^{2} - 9 x)

\frac{d}{d x} (6 x^{2} - 9 x) = 12 x - 9

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

= (12 x - 9) e^{x} + e^{x} (6 x^{2} - 9 x)

Vereinfache

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

= 6 e^{x} x^{2} + 3 e^{x} x - 9 e^{x}

\int \frac{t ^{3}}{m} - \frac{cos ( t )}{m} d t

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