derivative of ln(x/(x^2+5))

Lösung

\frac{d}{d x} (ln (\frac{x}{x ^{2} + 5}))

\frac{- x ^{2} + 5}{x ( x ^{2} + 5 )}

Schritte zur Lösung

\frac{d}{d x} (ln (\frac{x}{x ^{2} + 5}))

Wende die Kettenregel an:

\frac{1}{\frac{x}{x ^{2} + 5}} \frac{d}{d x} (\frac{x}{x ^{2} + 5})

= \frac{1}{\frac{x}{x ^{2} + 5}} \frac{d}{d x} (\frac{x}{x ^{2} + 5})

\frac{d}{d x} (\frac{x}{x ^{2} + 5}) = \frac{- x ^{2} + 5}{( x ^{2} + 5 ) ^{2}}

= \frac{1}{\frac{x}{x ^{2} + 5}} \cdot \frac{- x ^{2} + 5}{( x ^{2} + 5 ) ^{2}}

Vereinfache

\frac{1}{\frac{x}{x ^{2} + 5}} \cdot \frac{- x ^{2} + 5}{( x ^{2} + 5 ) ^{2}} : \frac{- x ^{2} + 5}{x ( x ^{2} + 5 )}

= \frac{- x ^{2} + 5}{x ( x ^{2} + 5 )}

\int - \frac{2}{t + 1} d t

9 x - 4 y x^{2} + 1 \frac{d y}{d x} = 0, y (0) = 2

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

\int \frac{2 x + 1}{( - 4 x ^{2} + 4 x + 3 ) ^{\frac{3}{2}}} d x

\frac{d}{d x} (sin (3 x + 2))