derivative y=(x^2-7x+7)e^{(9x)/7}

Lösung

ableitung von

y = (x^{2} - 7 x + 7) e^{\frac{9 x}{7}}

\frac{9 e ^{\frac{9 x}{7}} x ^{2}}{7} - 7 e^{\frac{9 x}{7}} x + 2 e^{\frac{9 x}{7}}

Schritte zur Lösung

\frac{d}{d x} ((x^{2} - 7 x + 7) e^{\frac{9 x}{7}})

Wende die Produktregel an:

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

f = x^{2} - 7 x + 7, g = e^{\frac{9 x}{7}}

= \frac{d}{d x} (x^{2} - 7 x + 7) e^{\frac{9 x}{7}} + \frac{d}{d x} (e^{\frac{9 x}{7}}) (x^{2} - 7 x + 7)

\frac{d}{d x} (x^{2} - 7 x + 7) = 2 x - 7

\frac{d}{d x} (e^{\frac{9 x}{7}}) = e^{\frac{9 x}{7}} \frac{9}{7}

= (2 x - 7) e^{\frac{9 x}{7}} + e^{\frac{9 x}{7}} \frac{9}{7} (x^{2} - 7 x + 7)

Vereinfache

(2 x - 7) e^{\frac{9 x}{7}} + e^{\frac{9 x}{7}} \frac{9}{7} (x^{2} - 7 x + 7) : \frac{9 e ^{\frac{9 x}{7}} x ^{2}}{7} - 7 e^{\frac{9 x}{7}} x + 2 e^{\frac{9 x}{7}}

= \frac{9 e ^{\frac{9 x}{7}} x ^{2}}{7} - 7 e^{\frac{9 x}{7}} x + 2 e^{\frac{9 x}{7}}

\int_{0}^{\infty} cos (x) d x

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