let-f-x-1-1-x-2-finf-f-n-x-

Question Number 104919 by mathmax by abdo last updated on 24/Jul/20

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

finf f^{(n)} (x)

Commented by malwaan last updated on 25/Jul/20

c a n y o u p o s t t h e s t e p s p l e a s e

t h a n k y o u s i r s h i k a r i

Commented by Dwaipayan Shikari last updated on 24/Jul/20

\frac{1.3.5.7 \dots (2 n - 1)}{2^{n}} . \frac{2^{n} x^{n}}{{(1 - x^{2})}^{n + \frac{1}{2}}} = \frac{1.3.5.7 . . (2 n - 1)}{{(1 - x^{2})}^{n + \frac{1}{2}}} . x^{n}

Commented by Dwaipayan Shikari last updated on 25/Jul/20

Prime causes double exponent: use braces to clarify

f^{^{″}} (x) = (- 1) \frac{1}{2} (- \frac{3}{2}) \frac{2 x . 2 x}{{(1 - x^{2})}^{\frac{5}{2}}}

S o

f^{n} (x) = \frac{1}{2} . \frac{3}{2} . \frac{5}{2} \dots . n \frac{2^{n} . x^{n}}{{(1 - x^{2})}^{n + \frac{1}{2}}} = (1.3.5 \dots . (2 n - 1)) \frac{x^{n}}{{(1 - x^{2})}^{n + \frac{1}{2}}}