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Q.
The derivative of the function $f(x)=x$ is
Limits and Derivatives
Solution:
It is easy to see that the derivative of the function $f(x)=x$ is the constant function 1. This is because
$f^{\prime}(x)=\displaystyle\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}=\displaystyle\lim _{h \rightarrow 0} \frac{x+h-x}{h}=\displaystyle\lim _{h \rightarrow 0} 1=1$