Question:
Find the derivative of x at x = 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 .
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