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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

\int \frac{sin ( y )}{cos ( y )} d y

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

x \to 1 lim (x - 1)

\int sec^{2} (x) + sec (2 x) tan (2 x) d x

d er i v a t i v e p (θ) = 7 θ