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Question
Find `bb(dy/dx)` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
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Solution
y = `sin^-1 ((2x)/(1 + x^2))`
Let, x = tan θ
⇒ θ = tan−1 x
∴ `y = sin^-1 ((2 tan theta)/(1 + tan^2 theta))`
= `sin^-1 (sin 2 theta) ... [because sin 2 theta = (2 tan theta)/(1 + tan^2 theta)]`
= 2 θ
y = 2 tan−1 x
∴ `dy/dx = 2 d/dx tan^-1 x`
`dy/dx = 2/(1 + x^2)`
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