Find the derivative of x at x = 1.
Question:

Find the derivative of at = 1.

Solution:

Let f(x) = x. Accordingly,

$f^{\prime}(1)=\lim _{h \rightarrow 0} \frac{f(1+h)-f(1)}{h}$

$=\lim _{h \rightarrow 0} \frac{(1+h)-1}{h}$

$=\lim _{h \rightarrow 0} \frac{h}{h}$

$=\lim _{b \rightarrow 0}(1)$

$=1$

Thus, the derivative of $x$ at $x=1$ is 1 .