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