derivative y=ln(1-x^2)

Lösung

ableitung von

y = ln (1 - x^{2})

- \frac{2 x}{1 - x ^{2}}

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

= - \frac{2 x}{1 - x ^{2}}

\frac{\partial}{\partial y} (2 y^{3} - 6 y + x^{2})

x \to + 0 + lim (\frac{1}{x} - \frac{1}{x ^{2} + x})

x \to 0 lim (x^{4} sin (\frac{4}{x}))

in v erse l a pl a ce \frac{1 + 4 s}{s ( 2 s ^{2} + 2 s + 1 )}

x \to 1 lim (\frac{x ^{5} - 1}{x - 1})