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)sin2x0sin(2x^2)|` . Find the value of `f^(prime)(0)dot`

If 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)sin2x0sin2x^2|,t h e n f(-2)=0 (b) f^(prime)(-1/2)=0 f^(prime)(-1)=-2 (d) f^(0)=4

If 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)],[sin2x,0,sin2x^2]| then find f'(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).

((sin x+cos x)^(2))/((sin x-cos x)^(2))

3-2cos x-4sin x-cos2x+sin2x=0

(sin x + cos x)^2 + (sin x - cos x)^2

if f(x)=cos(x) then find f'(x)=-6x cos^(2)(x^(2))sin(x)

If f(x)=|{:(5+sin^2x,cos^2x,4sin2x),(sin^2x,5+cos^2x,4sin2x),(sin^2x,cos^2x,5+4sin2x):}| then evaluate

Let f(x) = |(2cos^2x, sin2x, -sinx), (sin2x, 2 sin^2x, cosx), (sinx, -cosx,0)|, the value of int_0^(pi//2){f(x) + f'(x)} dx, is