The derivative of the function `cot^(-1){(cos2"x")^(1/2)}a tx=pi/6` is `(2/3)^(1/2)` (b) `(1/3)^(1/2)` (c) `3^(1/2)` (d) `6^(1/2)`

Explanation

`y = cot^-1 ( sqrt(cos 2x))`

`d/dx (cot^-1 x ) = -1/(1 +x^2) `

`dy/dx = d/dx (cot^-1sqrtcos2x) = -1/(1 + cos 2x) d/dx(sqrtcos2x)`

`d/dx(sqrtx) = 1/(2sqrtx) `

`-1/(1 + cos2x) *1/(2sqrt(cos2x)) d/dx (cos 2x) `

`= -1/(1+ cos 2x) xx 1/ (2sqrtcos 2x) xx (- sin2x xx2) `

`= (sin2x)/((1+ cos2x)sqrt(cos2x))`

`x= pi/6 `

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