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