Question

Nth defferential on e^tan^-1x

Answer 1

How can I find the nth derivative of tan−1xtan−1⁡x?

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Abhimanyu, B.E Electronics and Telecommunication Engineering & Mathematics Lover, University of Mumbai (2019)

Answered Dec 4, 2017

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Let y=tan^(-1)x

Differentiate w.r.t x,

y1= 1/(1+x^2) =1/(x^2-i^2) = 1/{(x-i)(x+i)} ……{i^2 =-1}

By partial fraction

y1=1/2i *[1/(x-i) - 1/(x+i) ] …………equation( 1)

{ note: if y=1/(ax+b) then,

yn= (-1)^n n! a^n /(ax+b)^(n+1)

}