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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

\frac{d}{d x} (\frac{x ^{2} - 1}{x ^{2} + 1}) = \frac{2 x}{x ^{2} - 1 ( x ^{2} + 1 ) ^{\frac{3}{2}}}

= \frac{1}{\frac{x ^{2} - 1}{x ^{2} + 1}} \cdot \frac{2 x}{x ^{2} - 1 ( x ^{2} + 1 ) ^{\frac{3}{2}}}

Vereinfache

\frac{1}{\frac{x ^{2} - 1}{x ^{2} + 1}} \cdot \frac{2 x}{x ^{2} - 1 ( x ^{2} + 1 ) ^{\frac{3}{2}}} : \frac{2 x}{( x ^{2} + 1 ) ( x ^{2} - 1 )}

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

\int_{0}^{1} 7 e^{x} - 7 x e^{x^{2}} d x

\frac{d}{d x} (sin (\frac{π}{2} x))

\int_{0}^{6} \frac{7 t}{( t - 7 ) ^{2}} d t

\int cos (4 x) cos (8 x) d x

y^{^{''}} - 4 y^{^{'}} - 12 y = 8 e^{- 2 x}