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

Lösung

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

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

Schritte zur Lösung

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

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

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

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

Vereinfache

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

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

y^{^{''}} - 4 y + 4 y = 0

y^{^{'}} = x (2 - y)

x \to - \infty lim (- 3 e^{x})

\frac{d}{d x} (x^{4} - 4 x^{2})

\int cos^{2} (2 θ) d θ