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Question
Find the derivatives of the following:
`cos^-1 ((1 - x^2)/(1 + x^2))`
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Solution
Let y = `cos^-1 ((1 - x^2)/(1 + x^2))`
Put x = tan θ
y = `cos^-1 ((1 - tan^2theta)/(1 + tan^2theta))`
y = cos-1 (cos 2θ)
y = 2θ
y = 2 tan-1x
`("d"y)/("d"x) = 2 xx 1/(1 + x^2)`
`("d"y)/("d"x) = 2/(1 + x^2)`
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