derivative of 8e^{2x}x+12e^{2x}

Lösung

\frac{d}{d x} (8 e^{2 x} x + 12 e^{2 x})

16 e^{2 x} x + 32 e^{2 x}

Schritte zur Lösung

\frac{d}{d x} (8 e^{2 x} x + 12 e^{2 x})

Wende die Summen-/Differenzregel an:

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

= \frac{d}{d x} (8 e^{2 x} x) + \frac{d}{d x} (12 e^{2 x})

\frac{d}{d x} (8 e^{2 x} x) = 8 (2 e^{2 x} x + e^{2 x})

\frac{d}{d x} (12 e^{2 x}) = 24 e^{2 x}

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

Vereinfache

8 (2 e^{2 x} x + e^{2 x}) + 24 e^{2 x} : 16 e^{2 x} x + 32 e^{2 x}

= 16 e^{2 x} x + 32 e^{2 x}

a re a 6 - x^{2}, 8 - 3 x

t an g e n t f (x) = \frac{e ^{2}}{x ^{2} - 2 x}, at x = - 2

\int_{- 1}^{1} 2 e^{x} d x

t an g e n t f (x) = \frac{2}{x - 3}, at x = 5

x \to \infty lim (\frac{( e ^{x} )}{2 x ^{2}})