Question

what is the nth derivative of tan inverse of (x/a) ?

Answer 1

The formula for the nth derivative of Tan inverse x/a is proved by mathematical induction.

Please see http://brainly.in/question/663103   or  http://brainly.in/question/741871 
for the proof.

$\frac{d^n}{dx^n}tan^{-1}\frac{x}{a}=\frac{(-1)^{n-1}(n-1)!}{\ (a^2+x^2)^{\frac{n}{2}}}Sin[n\ sin^{-1}(\frac{a}{\sqrt{a^2+x^2}})]$