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

let f(x) =(1/(√(1−x^2 )))  finf f^((n)) (x)

Commented bymalwaan last updated on 25/Jul/20

can you post the steps please  thank you sir shikari

Commented byDwaipayan Shikari last updated on 24/Jul/20

((1.3.5.7...(2n−1))/2^n ).((2^n x^n )/((1−x^2 )^(n+(1/2)) ))=((1.3.5.7..(2n−1))/((1−x^2 )^(n+(1/2)) )).x^n

Commented byDwaipayan Shikari last updated on 25/Jul/20

f^  ′(x)=(−1)(−(1/2))((2x)/((1−x^2 )^(3/2) ))  f^(′′) (x)=(−1)(1/2)(−(3/2))((2x.2x)/((1−x^2 )^(5/2) ))  So  f^n (x)=(1/2).(3/2).(5/2)....n((2^n .x^n )/((1−x^2 )^(n+(1/2)) ))=(1.3.5....(2n−1))(x^n /((1−x^2 )^(n+(1/2)) ))