derivative of (2-x/(1+2x^2))

Lösung

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

\frac{2 x ^{2} - 8 x - 1}{( 1 + 2 x ^{2} ) ^{2}}

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

\frac{d}{d x} (1 + 2 x^{2}) = 4 x

= \frac{( - 1 ) ( 1 + 2 x ^{2} ) - 4 x ( 2 - x )}{( 1 + 2 x ^{2} ) ^{2}}

Vereinfache

\frac{( - 1 ) ( 1 + 2 x ^{2} ) - 4 x ( 2 - x )}{( 1 + 2 x ^{2} ) ^{2}} : \frac{2 x ^{2} - 8 x - 1}{( 1 + 2 x ^{2} ) ^{2}}

= \frac{2 x ^{2} - 8 x - 1}{( 1 + 2 x ^{2} ) ^{2}}

x \to 0 lim (16 - 7 x)

\int - cos (x) + C d x

\frac{d}{d t} (4 e^{- t})

d er i v a t i v e 4 x^{2} - 2

\frac{d}{d x} (3 4 - \frac{1}{2} x)