Originally Posted by

**surjective** Hello,

If you would like to find the derivative of the function $\displaystyle f(x)= \sqrt{x}$, then perhaps you could follow the 3-step rule:

Let $\displaystyle f$ be a function and $\displaystyle x_{0}$ a point in the domain, then do as follows:

1) Compute $\displaystyle \triangle y=f(x_{0}+h)-f(x_{0})$

2) Compute and reduce $\displaystyle \frac{\triangle y}{h}=\frac{f(x_{0}+h)-f(x_{0})}{h}$

3) Let $\displaystyle h\to \infty$ in the reduced result from 2). If this limit exists then this limit will be the derivative, and the function $\displaystyle f$ differentiable.