pembuktian turunan fungsi cosinus

(f(x)=cos x maka f’(x)=-sin x)

f(x) =cos x

f(x+h) =cos(x+h)

cos A – COS B =  -2sin (A+B/2).sin (A-B/2)

f’(x) = lim     f(x+h) – f(x)/h

           h→0

         =   lim      cos(x+h) – cos x / h

           h→0

         =  - 2 sin {((x+h)+x)/2 .sin ((x+h) – x)/2}/ h

         =( - 2 sin 2x+h /2 . sin h/2) / h

        = lim      sin (2x+h) / 2  - 2 (sin h/2) / 2

            h→0

         = sin 2x/2  . -2.1/2

         f’(x) = sin x . -1

         f’(x)=  -sin x