Question

differentiate y=tan^-1[x+root(1+x^2)]

Answer 1

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Step-by-step explanation:

Given, y = tan-1(x/√(1 – x2))

Put x = sin θ

Then y = tan-1(sin θ/√(1 – sin2 θ))

= tan-1(sin θ/√cos2 θ)

= tan-1(sin θ/cos θ)

= tan-1 tan θ

= θ

= sin-1 x

Differentiate w.r.t.x

dy/dx = 1/√(1 – x2)