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Question
Differentiate the following w.r.t.x:
`sqrt(cosx) + sqrt(cossqrt(x)`
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Solution
Let y = `sqrt(cosx) + sqrt(cossqrt(x)`
Differentiating w.r.t. x, we get
`"dy"/"dx" = "d"/"dx"[sqrt(cosx) + sqrt(cossqrt(x))]`
= `"d"/"dx"(cosx)^(1/2) + "d"/"dx"(cossqrt(x))^(1/2)`
= `1/2(cosx)^(-1/2)."d"/"dx"(cosx) + 1/2(cossqrt(x))^(-1/2)."d"/"dx"(cossqrt(x))`
= `(1)/(2sqrt(cosx)).(-sinx) + (1)/(2sqrt(cossqrt(x))) xx (-sinsqrt(x))."d"/"dx"(sqrt(x))`
= `(-sinx)/(2sqrt(cosx)) - (sinsqrt(x))/(2sqrt(cossqrt(x))) xx (1)/(2sqrt(x)`
= `(-sinx)/(2sqrt(cosx)) - (sinsqrt(x))/(4sqrt(x)sqrt(cossqrt(x)`
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