Suppose $f(x) = x$.

By the first principle we have,

${{\text{f}}^\prime }({\text{x}}) = \mathop {\lim }\limits_{{\text{h}} \to 0} \frac{{{\text{f}}({\text{x}} + {\text{h}}) – {\text{f}}({\text{x}})}}{{\text{h}}}$

Substituting $x = 1$ to get,

Then,

${f^\prime }(1) = \mathop {\lim }\limits_{h \to 0} \frac{{f(1 + h) – f(1)}}{h}$

${f^\prime }(1) = \mathop {\lim }\limits_{h \to 0} \frac{{(1 + h) – 1}}{h}$

${f^\prime }(1) = \mathop {\lim }\limits_{h \to 0} \frac{{1 + h – 1}}{h}$

${f^\prime }(1) = \mathop {\lim }\limits_{h \to 0} \frac{h}{h}$

${f^\prime }(1) = \mathop {\lim }\limits_{h \to 0} 1$

${f^\prime }(1) = 1$