derivative of ln((arcsin(x)^2))

Lösung

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

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

Schritte zur Lösung

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

Wende die Kettenregel an:

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

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

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

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

Vereinfache

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

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

d er i v a t i v e \frac{140000}{x}

\int \frac{1}{x ^{2} - 3 x - 15} d x

\int 40 + 6 x - x^{2} d x

\int \frac{1}{x ( I n x ) ^{2}} d x

\frac{d}{d x} (tan (x) d x)