What is the nth derivative of tan inverse x/a
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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}})]](https://tex.z-dn.net/?f=%5Cfrac%7Bd%5En%7D%7Bdx%5En%7Dtan%5E%7B-1%7D%5Cfrac%7Bx%7D%7Ba%7D%3D%5Cfrac%7B%28-1%29%5E%7Bn-1%7D%28n-1%29%21%7D%7B%5C+%28a%5E2%2Bx%5E2%29%5E%7B%5Cfrac%7Bn%7D%7B2%7D%7D%7DSin%5Bn%5C+sin%5E%7B-1%7D%28%5Cfrac%7Ba%7D%7B%5Csqrt%7Ba%5E2%2Bx%5E2%7D%7D%29%5D "\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}})]")
Please see http://brainly.in/question/663103 or http://brainly.in/question/741871
for the proof.
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