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Question
If y = `sqrt(tansqrt(x)`, find `("d"y)/("d"x)`.
Solution
y = `sqrt(tansqrt(x)`
Differentiating w.r.t. x, we get
`("d"y)/("d"x) = "d"/("d"x)(sqrt(tansqrt(x)))`
= `1/(2sqrt(tansqrt(x)))*"d"/("d"x)(tansqrt(x))`
= `1/(2sqrt(tansqrt(x)))*sec^2(sqrt(x))*"d"/("d"x)(sqrt(x))`
= `(sec^2sqrt(x))/(2sqrt(tansqrt(x)))*1/(2sqrt(x))`
∴ `("d"y)/("d"x) = (sec^2sqrt(x))/(4sqrtxsqrt(tansqrt(x))`
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