Find the derivative of $x$ using the definition. Apply the definition of the derivative: $\displaystyle f'(x)=\lim_{h\to0}\frac{f(x+h)-f(x)}{h}$. The function $f(x)$ is the function we want to differentiate, which is $x$. Substituting $f(x+h)$ and $f(x)$ on the limit, we get

Cancel like terms $x$ and $-x$

Simplify the fraction $\frac{h}{h}$ by $h$

The limit of a constant is just the constant