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

Lösung

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

e^{x} x^{2} + 4 e^{x} x + 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} + 4 e^{x} x + 2 e^{x}

= e^{x} x^{2} + 4 e^{x} x + 2 e^{x}

t an g e n t x^{2} + 2 x y - y^{2} + x = 51, (5, 7)

s l o p e (4.3) (4.6)

\int e^{- x} + e^{- 3 x} d x

n = 0 \sum \infty \frac{n !}{n ^{n}}

\int (\frac{1}{x ^{9}} - x^{9} - \frac{1}{8}) d x