derivative of (e^{2x}/(1+x^2))

Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{1 + x ^{2}})

\frac{e ^{2 x} \cdot 2 ( 1 + x ^{2} ) - 2 x e ^{2 x}}{( 1 + x ^{2} ) ^{2}}

Schritte zur Lösung

\frac{d}{d x} (\frac{e ^{2 x}}{1 + x ^{2}})

Wende die Quotientenregel an:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{\frac{d}{d x} ( e ^{2 x} ) ( 1 + x ^{2} ) - \frac{d}{d x} ( 1 + x ^{2} ) e ^{2 x}}{( 1 + x ^{2} ) ^{2}}

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

\frac{d}{d x} (1 + x^{2}) = 2 x

= \frac{e ^{2 x} \cdot 2 ( 1 + x ^{2} ) - 2 x e ^{2 x}}{( 1 + x ^{2} ) ^{2}}

\frac{d}{d x} (\frac{x}{2 - x ^{2}})

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

s l o p e (- 5.2) (2.5)

\frac{d}{d x} (sin (x + x) + 5)

\frac{\partial}{\partial x} (6 + x ln (x y - 9))