(d)/(dx)(cos x-cos y)^(2)+((sin t)/(sin x)-sin y)^(2)=4cos^(2)(x+y)/(2)

d/(dx) (sin x+ cos x)

(d)/(dx)(sin^(2)x+cos^(2)x) =

(d)/(dx)[cos^(2)x(3-4cos^(2)x)^(2)]+(d)/(dx)[sin^(2)(3-4sin^(2)x)^(2)]=

d/(dx)[sin {2 cos^(-1) (sin x)}] =

d/(dx)[sin {2 cos^(-1) (sin x)}] =

(d)/(dx)(cos (x/2))= (A) (1)/(2)sin(x)/(2) , (B) -(1)/(2)cos(x)/(2) (C) -(1)/(2)sin(x)/(2) , (D) -sin(x)/(4)

(d)/(dx)[(sin x)/(1+cos x)]=

If x in(0,(pi)/(2)), thenshowthat(d)/(dx)cos^(-1){(7)/(2)(1+cos2x)+(sqrt(sin^(2)x-48cos^(2)x))sin x}=1+(7sin x)/(sqrt(sin^(2)-48cos^(2)x))

d/dx (sin x)^(cos x) =

(d)/(dx)[3(sin^(2)x+cos^(2)x)]=