derivative of (e^x/(2x^2))

Lösung

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

\frac{e ^{x} ( x - 2 )}{2 x ^{3}}

Schritte zur Lösung

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

Entferne die Konstante:

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

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

\frac{1}{2} \cdot \frac{e ^{x} x ^{2} - 2 x e ^{x}}{( x ^{2} ) ^{2}} : \frac{e ^{x} ( x - 2 )}{2 x ^{3}}

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

\int 1 - sin^{2} (x) d x

\frac{d}{d x} (16 + x)

x \to 0 lim (2^{- x})

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

t an g e n t f (x) = x^{s i n (x)}, (\frac{π}{2}, \frac{π}{2})