If `y=cos^(-1)(cosx),t h e n(dy)/(dx)` at x=`(5pi)/4` is equal to (a)1 (b)-1 (c)0 (d)4

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 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 y=(log)_(sinx)(tanx),t h e n(((dy)/(dx)))_(pi/4)"is equal to" (a) 4/(log2) (b) -4log2 (c) (-4)/(log2) (d) none of these

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

If (sinx)(cosy)=1/2, then (d^2y)/(dx^2) at (pi/4,pi/4) is (a) -4 (b) -2 (c) -6 (d) 0

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 ln((e-1)e^(xy) +x^2)=x^2+y^2 then ((dy)/(dx))_(1,0) is equal to

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

The value of sin^(-1)("cos"(cos^(-1)(cosx)+sin^(-1)(sinx))), where x in (pi/2,pi) , is equal to (a) pi/2 (b) -pi (c) pi (d) -pi/2