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