f(x) = x^2 -1/2 * cos(x) <~the problem

solution:

Multiply -1 by cos to get -cos(x)

x^2 - cos(x)(1)/2 <~this two

d/dx(x^2) = 2x

d/dx(cos(x)(1)/2) = sin(x)*1+(-cos(x))*0 = sin(x)+0 = sin(x)

d/dx (x^2 -1/2 * cos(x)) = 2x+sin(x)

My question is what happened to the two in the denominator? We never worked with it. but if you take the derivitive of the 2 it's zero and anything divided by 0 is undef.... Right??