Not Understanding Proof for Derivative.
If y' = f'(x)
Then y = f(x) in one integral.
Now Let g(x) be any other integral in y' = f'(x) that is g'(x) = f'(x). Show that g(x) can differ from f(x) by at most a constant
Then Let : w' = f'(x) - g'(x) = 0
Then the equation of w as a function of x must be w = constant
hence we see that w = f(x) - g(x) equals g(x) = f(x) + constant.
Because g(x) is any integral other than f(x) all integrals are given by y = f(x) + c
How did they get from w = constant to g(x) = f(x) + constant algebraically?
second.... they said Now Let g(x) be any other integral in y' = f'(x) that is g'(x) = f'(x). But if they are two dif integrals why did they set g'(x) = f'(x)? Doesn't setting something equal to something mean they are equal? Is there something that I am misunderstanding?