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