derivative 10(2e^{x^2}x^2+e^{x^2})

Lösung

ableitung von

10 (2 e^{x^{2}} x^{2} + e^{x^{2}})

10 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

Schritte zur Lösung

\frac{d}{d x} (10 (2 e^{x^{2}} x^{2} + e^{x^{2}}))

Entferne die Konstante:

(a \cdot f)^{'} = a \cdot f^{'}

= 10 \frac{d}{d x} (2 e^{x^{2}} x^{2} + e^{x^{2}})

Wende die Summen-/Differenzregel an:

(f \pm g)^{'} = f^{'} \pm g^{'}

= 10 (\frac{d}{d x} (2 e^{x^{2}} x^{2}) + \frac{d}{d x} (e^{x^{2}}))

\frac{d}{d x} (2 e^{x^{2}} x^{2}) = 2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x)

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

= 10 (2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x)

Multipliziere aus

2 (2 e^{x^{2}} x^{3} + 2 e^{x^{2}} x) + e^{x^{2}} \cdot 2 x : 4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x

= 10 (4 e^{x^{2}} x^{3} + 6 e^{x^{2}} x)

n = 1 \sum \infty \frac{5 n}{n !}

\frac{d}{d x} ((\frac{x}{5} - \frac{5}{x})^{5})

\int_{0}^{2} (2 x - 3) (4 x^{2} + 1) d x

t an g e n t f (x) = 4 x^{2} + 4 x - 2, at x = - 1

\frac{d}{d x} ((x^{3} + 5) e^{x})