derivative of ln((x-2/(x+2)))

Lösung

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

\frac{4}{( x - 2 ) ( x + 2 )}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= \frac{4}{( x - 2 ) ( x + 2 )}

3 y^{^{''}} - 10 y^{^{'}} + 3 y = 0, y (0) = - 5, y^{^{'}} (0) = - 1

\int_{0}^{π} sin^{2} (x) cos (x) d x

t an g e n t f (x) = (6 x - 5)^{\frac{1}{2}}, at x = 1

\frac{d y}{d x} = 8 x^{- 9}

\frac{d}{d x} (\frac{2}{3} x^{3} - \frac{3}{4 x ^{2}})