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Question
Find `dy/dx` in the following:
`y = sin^(-1)((2x)/(1+x^2))`
Solution
y = `sin^-1 ((2x)/(1 + x^2))`
Let, x = tan `theta => theta = tan^-1 x`
`therefore 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 theta`
`y = 2 tan^-1 x`
`therefore dy/dx = 2 d/dx tan^-1 x`
`dy/dx = 2/(1 + x^2)`
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