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Grade 12Differential Calculus

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

(1+x²)^1/2+ (1-x²)^1/2

Aby Alex

16 Years agoGrade 12

2 Answers

Pankaj

12 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

12 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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