derivative of e^{arcsin(x})

Lösung

\frac{d}{d x} (e^{a r c s i n (x)})

\frac{e ^{a r c s i n (x)}}{1 - x ^{2}}

Schritte zur Lösung

\frac{d}{d x} (e^{a r c s i n (x)})

Wende die Kettenregel an:

e^{a r c s i n (x)} \frac{d}{d x} (arcsin (x))

= e^{a r c s i n (x)} \frac{d}{d x} (arcsin (x))

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

= e^{a r c s i n (x)} \frac{1}{1 - x ^{2}}

Vereinfache

e^{a r c s i n (x)} \frac{1}{1 - x ^{2}} : \frac{e ^{a r c s i n (x)}}{1 - x ^{2}}

= \frac{e ^{a r c s i n (x)}}{1 - x ^{2}}

x \to 2 lim (x^{2} + 3 x)

\int arccos (3 x) d x

d er i v a t i v e f (x) = 3 x^{3}

\int sin^{2} (3 x) \cdot cos^{4} (3 x) d x

\int \frac{2 x ^{2} - 5 x - 18}{x ^{3} + x ^{2} - 6 x} d x