derivative of e^xx^3+6e^xx^2+6e^xx

Lösung

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

e^{x} x^{3} + 9 e^{x} x^{2} + 18 e^{x} x + 6 e^{x}

Schritte zur Lösung

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

Wende die Summen-/Differenzregel an:

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

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

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

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

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

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

Vereinfache

e^{x} x^{3} + 3 x^{2} e^{x} + 6 (e^{x} x^{2} + 2 x e^{x}) + 6 (e^{x} x + e^{x}) : e^{x} x^{3} + 9 e^{x} x^{2} + 18 e^{x} x + 6 e^{x}

= e^{x} x^{3} + 9 e^{x} x^{2} + 18 e^{x} x + 6 e^{x}

y^{2} d x - (1 - x) d y = 0

x \to 0 lim (3)

\frac{d}{d x} (- 3 x^{5} + 4 x^{- 3} - 5 x^{- 2} + 5)

x \to \infty lim (\frac{x}{2 a})

\frac{\partial}{\partial x} (\frac{x}{R ( x )})