derivative of ln(arcsin(x^2))

Lösung

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

\frac{2 x}{arcsin ( x ^{2} ) 1 - x ^{4}}

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 x}{1 - x ^{4}}

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

Vereinfache

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

= \frac{2 x}{arcsin ( x ^{2} ) 1 - x ^{4}}

\int (x^{3} - 6 x) d x

\frac{d}{d x} (x^{3} - 6 x^{2} - 15 x + 40)

x \to 0 lim (- \frac{7}{1 - 7 x})

a re a y = x^{2} + 2, (1, 4)

t an g e n t y = 9 cos (x), (\frac{π}{3}, 4.5)