We use the limit definition, putting in *x* instead of *a*: Therefore *f'*(*x*) = 2*x*. If we plug in 1 for *x* we find *f'*(1) = 2, which agrees with our earlier calculation. In formulas, the limit definition of the derivative function is This is the same as the limit definition of the derivative of a point, but with *x* instead of *a*. When we evaluate the derivative of *f* at a point, we take a value and plug it in for *x* in the definition above. |