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

Lösung

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

6 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Summen-/Differenzregel an:

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

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

\frac{d}{d x} (4 e^{x^{2}} x^{3}) = 4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2})

\frac{d}{d x} (6 e^{x^{2}} x) = 6 (2 e^{x^{2}} x^{2} + e^{x^{2}})

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

Multipliziere aus

4 (2 e^{x^{2}} x^{4} + 3 e^{x^{2}} x^{2}) + 6 (2 e^{x^{2}} x^{2} + e^{x^{2}}) : 8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}}

= 6 (8 e^{x^{2}} x^{4} + 24 e^{x^{2}} x^{2} + 6 e^{x^{2}})

5 x^{^{''}} + 5 x^{^{'}} + 6 x = 0, x^{^{'}} (0) = 0.45, x (0) = - 0.3

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