derivative of (x^2-2xe^x)

Lösung

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

e^{x} x^{2} - 2 e^{x}

Schritte zur Lösung

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

Wende die Produktregel an:

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

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

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

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

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

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

Vereinfache

(2 x - 2) e^{x} + e^{x} (x^{2} - 2 x) : e^{x} x^{2} - 2 e^{x}

= e^{x} x^{2} - 2 e^{x}

\int x sin (- 3 x) d x

\int ln (x^{2} + 1) d x

l a pl a ce t r an s f or m e^{2 t} sin (5 t)

\int_{0}^{\frac{π}{2}} - 2 sin^{2} (3 x) d x

(\frac{d y}{d x}) = 0.011 \cdot y \cdot (2 - (y - 25))