Find the differentiation of the function tan 1 radic 1 x2 x ........

Mathematics (NDA) Diffrentiation

Find the differentiation of the function tan-1√(1+x²)+x ?

- 1/2 (1/1+x²)

1/2 (1/1+x²)

1/2 (1/1-x²)

(1/1-x²)

Y=tan^-1√(1+x²)+x

put x= cot θ

y=tan^-1√(1+ cot²θ)+ cotθ

= tan^-1 √cosec² θ +cot θ

= tan^-1 cosec θ +cot θ

= tan^-1(1+cos θ /sinθ)

= tan^-1 (2 cos ²θ/2 /2sinθ/2 cos θ/2)

= tan^-1 (cot θ/2)

= tan^-1 (tan π/2 –θ/2)

=π/2 -θ/2

= π/2 -1/2cot^-1 x

Differentiating w. r. to x

dy/dx =0 -1/2 (- 1/1+x²)

=1/2 (1/1+x²)

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