" 23) "quad " cot "^(-1){(cos2x)^(1/2)}quad " at "x=pi/6

The derivative of the function cot^(-1){(cos2x)^(1//2)} at x=pi//6 is (a) (2//3)^(1//2) (b) (1//3)^(1//2) (c) 3^(1//2) (d) 6^(1//2)

The derivative of the function cot^(-1){(cos2x)^((1)/(2))} at x=(pi)/(6) is ((2)/(3))^((1)/(2))(b)((1)/(3))^((1)/(2))(c)3^((1)/(2))(d)6^((1)/(2))

The derivative of the function cot^(-1){(cos2x)^(1/2)} at x=pi/6 is (2/3)^(1/2) (b) (1/3)^(1/2)(c)3^(1/2)(d)6^(1/2)

If f(x)=cot^(-1)(cos2x)^(1//2) , then f'(pi//6) is :

If f(x)=cot^(-1)sqrt(cos2x)," then: "f'((pi)/(6))=

If f(x)=cot^(-1)sqrt(cos2x)," then: "f'((pi)/(6))=

int_(-(pi)/(3))^(0)[cot^(-1)((2)/(2cos x-1))+cot^(-1)(cos x-(1)/(2))]dx is equal to (pi^(2))/(6) (b) (pi^(2))/(3) (c) (pi^(2))/(8) (d) (3 pi^(2))/(8)

The differential coeffcient of cot^(-1)(sqrtcos2x)at x = (pi)/(6) is