If `int f(x)cos xdx=(1)/(2)f^(2)(x)+C" ,then "f(x)" can be "P sin x`.Find the value of "P

If intf(x)cos x dx = 1/2 f^(2)(x)+C , then f(x) can be

If intf(x)sec^(2)xdx=(1)/(2)[f(x)]^(2)+c, then : f(x) can be

If int f(x)cos xdx=(1)/(2)f^(2)(x)+C then the value of 4f(x) at x=0 is

If int(x+sin x)/(1+cos x)dx=f(x)tan g(x)+C , then, f(x)=

If int cos ec2xdx=f(g(x))+c, then

If int(1)/(sin(x-a)cos(x-a))dx=log[f(x)]+c , then f(x)=

f=int(cos^(5)xdx)/ sin^(3)x

"Let "f(x)=|{:(cos(x+x^(2)),sin (x+x^(2)),-cos(x+x^(2))),(sin (x-x^(2)),cos (x-x^(2)),sin (x-x^(2))),(sin 2x, 0, sin (2x^(2))):}|. Find the value of f'(0).