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

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

= 2 (\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

= 2 (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

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

x \to 5 lim (\frac{2}{x - 3})

s l o p e (2.4) (3.8)

\int (x x - 1) d x

\frac{d}{d θ} (e^{θ})

f (x) = (e^{- x} - e^{3}) (e^{x} + e^{- 5})