How to find the derivative of sqrt(x) from first principles?

Graphical explanation leading to the expression that we need to develop (Lim(a->0) (sqrt(x+a) - sqrt(a))/(a). Then we need to understand how to rearrange a fraction involving square roots (multiplication by sqrt(a+x) + sqrt(a) on the nominator and denominator). Calculation of limits to get 1/2sqrt(x).