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

Lösung

ableitung von

\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}}

Multipliziere aus

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

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

\int_{- \infty}^{0} \frac{z}{z ^{4} + 4} d z

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

x \to \infty + lim (sec (x))

\int \frac{( x + 6 )}{5 - 4 x - x ^{2}} d x

y^{^{''}} + y^{^{'}} = 0, y (0) = 2, y^{^{'}} (0) = 1