derivative f(x)=(e^x)/(x^2+1)

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

\int (7 x^{2}) e^{x^{3} + 1} d x

\int e^{- 2 y} y d y

t an g e n t f (x) = - x^{3} + x^{2} + 4 x - 2, at x = 0

\frac{\partial}{\partial y} (y e^{x y} sin (y))

x \to 2 - lim (3 x)