limit for h approaching 0 of 2 * cos( x + h/2 ) * sin( h/2 ) / h

for h approaching 0 on sin(h)~= h we divide both denominator and numerator by 2 to match the contents as we can see it will be 1 ence sin(h/2)/(h/2) ~= (h/2)/(h/2) -> 1 when h approaching 0 remains cos(x+h/2) that for h = 0 is cos(x)