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

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

= \frac{1}{\frac{x ^{2} - 2}{x ^{2} + 2}} \cdot \frac{4 x}{x ^{2} - 2 ( x ^{2} + 2 ) ^{\frac{3}{2}}}

Vereinfache

\frac{1}{\frac{x ^{2} - 2}{x ^{2} + 2}} \cdot \frac{4 x}{x ^{2} - 2 ( x ^{2} + 2 ) ^{\frac{3}{2}}} : \frac{4 x}{( x ^{2} + 2 ) ( x ^{2} - 2 )}

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

\frac{d}{d x} (- 5 x^{\frac{4}{5}} + 3 x^{\frac{2}{3}} + 2)

x \to 9 lim (\frac{∣ x - 9 ∣}{x - 9})

\frac{\partial}{\partial x} (\frac{2 y}{3 x})

(x^{2} e^{x} + y) d x = x d y

in v erse l a pl a ce \frac{s}{s ^{2} + 3 s + 2}