derivative f(x)=(9x^2-15x)e^x

Lösung

ableitung von

f (x) = (9 x^{2} - 15 x) e^{x}

9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

Schritte zur Lösung

\frac{d}{d x} ((9 x^{2} - 15 x) e^{x})

Wende die Produktregel an:

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

f = 9 x^{2} - 15 x, g = e^{x}

= \frac{d}{d x} (9 x^{2} - 15 x) e^{x} + \frac{d}{d x} (e^{x}) (9 x^{2} - 15 x)

\frac{d}{d x} (9 x^{2} - 15 x) = 18 x - 15

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

= (18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x)

Vereinfache

(18 x - 15) e^{x} + e^{x} (9 x^{2} - 15 x) : 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

= 9 e^{x} x^{2} + 3 e^{x} x - 15 e^{x}

\int sin (x) cos (x) ln (sin (x)) d x

\int_{0}^{1} 4 - x^{2} d x

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d er i v a t i v e f (x) = \frac{1}{2} (x + 1)^{- \frac{1}{2}}