If `y = { sin "" (x)/(2) sin "" (x ^(2))/(2 ^(2)) . sin "" (x ^(3))/(2 ^(3)).....sin "" (x ^(n))/(2 ^(n))}` then `(dy)/(dx)=`

If y = sin^(2).(x)/(2) , then (dy)/(dx) =

If y =sin (x^(2) +x) ,then (dy)/(dx) =

If y = sin^(2)(x/2) , then (dy)/(dx) is-

(dy/dx)+(y/x)=sin x^(2)

If y= 2 ^(sin x) -sin ^(2)x ,then (dy)/(dx) =

If y=cos (x^(3)) sin ^(2) (x^(5)),then (dy)/(dx) =

If f_(n)(x) = (sin x)/(cos3x)+(sin 3x)/(cos 3^(2)x) +(sin 3^(2)x)/(cos 3^(3)x) +....+ (sin 3^(n-1)x)/(cos 3^(n)x)"Then" f_(2) ((pi)/(4)) + f_(3) ((pi)/(4))=

If sin ((x+y)/( 2)) =sinx +sin y and sin ((x-y)/( 2 ))ne 0,then (dy)/(dx)=

If y=3x^(3)sin^(-1)x+(x^(2)+2)sqrt(1-x^(2)), then (dy)/(dx)=

Find the period of f(x)=sin x+tan(x)/(2)+sin(x)/(2^(2))+tan(x)/(2^(3))+...+sin(x)/(2^(n-1))+tan(x)/(2^(n))