derivative of (sqrt(x)/(x-2sqrt(x)))

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

x \to - 1 lim (2 x^{2} + 6 x - 1)

x \to 2 lim (\frac{5}{∣ 2 - x ∣})

\frac{d}{d x} (e^{- \frac{x}{a}})

f (x) = e^{x} arctan (x)

f a c t or 2 sin (x) + sin^{2} (x)