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Question
Find `dy/dx` in the following:
`y = cos^(-1) ((1-x^2)/(1+x^2)), 0 < x < 1`
Solution
y = `cos^-1 ((1 - x^2)/(1 + x^2))`
Let, `x = tan theta => theta = tan^-1 x`
`therefore y = cos^-1 ((1 - tan^2 theta)/(1 + tan^1 theta))`
`= cos^-1 (cos 2 theta)`
`= 2 theta`
`y = 2 tan^-1 x`
`dy/dx = 2 d/dx tan^-1 x`
`dy/dx = 2/(1 + x^2)`
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