If `y=tan^(-1)((2^x)/(1+2^(2x+1))),t h e n(dy)/(dx)a tx=0` is (a)1 (b) 2 (c) 1n 2 (d) none of these

If f^(prime)(x)=sqrt(2x^2-1)a n dy=f(x^2),t h e n(dy)/(dx)a tx=1 is 2 (b) 1 (c) -2 (d) none of these

If e^x=(sqrt(1+t)-sqrt(1-t))/(sqrt(1+t)+sqrt(1-t))a n dtany/2=sqrt((1-t)/(1+t)) ,then (dy)/(dx) at t=1/2 is (a) -1/2 (b) 1/2 (c) 0 (d) none of these

If y="sec"(tan^(-1)x),t h e n(dy)/(dx)a tx=1 is (a) cospi/4 (b) sinpi/2 (c) sinpi/6 (d) cospi/3

If |cos^(-1)((1-x^2)/(1+x^2))|

If y=(1+x)(1+x^2)(1+x^4)......(1+x^(2n)), then find (dy)/(dx)a tx=0.

If y=(sin^(-1)x)/(sqrt(1-x^2)),t h e n((1-x^2)dy)/(dx) is equal to (a) x+y (b) 1+x y (c) 1-x y (d) x y-2

If x^2+y^2+z^2=r^2,t h e ntan^(-1)((x y)/(z r))+tan^(-1)((y z)/(x r))+tan^(-1)((x z)/(y r)) is equal to (a) pi (b) pi/2 (c) 0 (d) none of these

If y=|cosx|+|sinx|,t h e n(dy)/(dx)a tx=(2pi)/3 is (1-sqrt(3))/2 (b) 0 (c) 1/2(sqrt(3)-1) (d) none of these

If x_1=2tan^(-1)((1+x)/(1-x)),x_2=sin^(-1)((1-x^2)/(1+x^2)) , where x in (0,1), then x_1+x_2 is equal to 0 (b) 2pi (c) pi (d) none of these

If y=cos^(-1)((2x)/(1+x^2)),t h e n(dy)/(dx)i s (a) (-2)/(1+x^2) for all x (b) (-2)/(1+x^2) for all |x| 1 (d) none of these