y = 1/2 x^2
y' = 1/2 * (2x) = x
In fact,
y = x^2+c
has y' = x for any constant c.
For proof, are you looking for the derivative using the definition of the limit? If so, I'm sure you've seen the work before.
Find the function that would produce a derivative of y = x. Prove your results.
1 answer