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

Lösung

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

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

Schritte zur Lösung

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

Wende die Quotientenregel an:

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

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

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

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

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

Vereinfache

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

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

\int (π - x) cos (π x) d x

x \to 1 lim (\frac{x - 1}{x ^{3} - 1})

y^{^{''}} - 4 y^{^{'}} - 12 y = 0

d er i v a t i v e 2 y

im pl i c i t \frac{d y}{d x}, y = arccos (4 x^{2})