Chapter CR, Problem 11E

Find each limit, if it exists. If a limit does not exist, state that fact.

If $f\left(x\right)=x^2+3,$ find $f\text{'}\left(x\right)$ by determining $\underset{h\to 0}{\lim }\frac{f\left(x+h\right)-f\left(x\right)}{h}$.