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