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Differentiate tan −1 [ (1+x 2 ) 1/2 - (1-x 2 ) 1/2 ] w.r.t x ? (1+x 2 ) 1/2 + (1-x 2 ) 1/2

Differentiate tan−1   [ (1+x2)1/2 - (1-x2)1/2 ]  w.r.t x ?



 



                              (1+x2)1/2 + (1-x2)1/2

Grade:12

2 Answers

Pankaj
askIITians Faculty 131 Points
9 years ago
I am not able to interpret your query. Please write down the problem clearly so that I can provide you the meaningful answer.
Thanks & Regards
Pankaj Singh
askIITians Faculty
Arun Kumar IIT Delhi
askIITians Faculty 256 Points
9 years ago
Hello Student,
\\\frac{d}{du}\left(\arctan \left(u\right)\right) \\\frac{1}{u^2+1}x\left(\frac{1}{\sqrt{x^2+1}}+\frac{1}{\sqrt{1-x^2}}\right) \\u=\sqrt{1+x^2}-\sqrt{1-x^2} \\=\frac{1}{\left(\sqrt{1+x^2}-\sqrt{1-x^2}\right)^2+1}x\left(\frac{1}{\sqrt{x^2+1}}+\frac{1}{\sqrt{1-x^2}}\right) \\=\frac{x\left(\sqrt{1-x^2}+\sqrt{x^2+1}\right)}{2x^4+3\sqrt{1-x^4}-2}
Thanks & Regards
Arun Kumar
Btech, IIT Delhi
Askiitians Faculty

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