derivative ln(ln(x/(2-x^2)))

Lösung

ableitung von

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

x \to 5 lim (x^{2} - 3 x - 10)

\frac{d y}{d x} = 5 x y

\frac{\partial}{\partial x} (y^{2} - 2 x y - 2 x^{2})

d er i v a t i v e f (x) = 5 x + 7

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