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=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 f(x)=|sinx|+|cosx|, then the value f(x)^'a tx=(7pi)/6 is (a)positive (b) (1-sqrt(3))/2 (c)0 (d) none of these

If y=cos(sinx^(2)), " then " (dy)/(dx) " at " x=sqrt(pi/2) is

If y=tan^(-1)sqrt((x+1)/(x-1)),t h e n(dy)/(dx)i s (-1)/(2|x|sqrt(x^2-1)) (b) (-1)/(2xsqrt(x^2-1)) 1/(2xsqrt(x^2-1)) (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=(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

The solution for x of the equation int_(sqrt(2))^x(dt)/(tsqrt(t^2-1))=pi/2 is pi (b) (sqrt(3))/2 (c) 2sqrt(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 sinx+cosx=(sqrt(7))/2, where x in 1s t quadrant, then tanx/2 is equal to (a) (3-sqrt(7))/3 (b) (sqrt(7)-2)/3 (c) (4-sqrt(7))/4 (d) none of these

The equation of the curve is y=f(x)dot The tangents at [1,f(1),[2,f(2)],a n d[3,f(3)] make angles pi/6,pi/3,a n dpi/4, respectively, with the positive direction of x-axis. Then the value of int_2^3f^(prime)(x)f^(x)dx+int_1^3f^(x)dx is equal to (a) -1/(sqrt(3)) (b) 1/(sqrt(3)) (c) 0 (d) none of these