derivative of arcsin(sqrt(1-x^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

a re a y = 2, y = sin (x), x = 0, x = π

in v erse l a pl a ce \frac{5}{( s ) ( s ^{2} + s + 2 )}

x = 1 \sum \infty \frac{( ( 2 x ) ^{x} )}{x ^{2 x}}

\int \frac{2 x}{π} d x

l a pl a ce t r an s f or m t^{6}