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

(d)/(dx)sin x

why (d)/(dx)sin x=cos x?

The differentiation of sin x with respect to x is cos x* i.e.(d)/(dx)(sin x)=cos x

Number of solution of the equation (d)/(dx)int_(cos x)^( sin x)(dt)/(1-t^(2))=2sqrt(2)in[0,pi] is

" Q."3 (d)/(dx){(sin x+cos x)/(sqrt(1+sin2x))} =

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

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

(d)/(dx)sin^(2)x

The differentiation of cos x with respect to x is -sin x. i.e.(d)/(dx)(cos x)=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)