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Question
Differentiate the following w. r. t. x.
cos–1(1 – x2)
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Solution
Let y = cos–1(1 – x2)
Differentiating w.r.t. x, we get
`(dy)/(dx) = d/(dx) [cos^-1 (1 - x^2)]`
= `(-1)/(sqrt(1 - (1 - x^2)^2)) * d/(dx)(1 - x^2)`
= `(-1)/(sqrt(1 - (1 - 2x^2 + x^4))) * (0 - 2x)`
= `(2x)/(sqrt(2x^2 - x^4))`
= `(2x)/(xsqrt(2 - x^2))`
= `2/(sqrt2 - x^2)`
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