Answer
The derivative is not always the limit. The limit is not always the derivative.
Work Step by Step
For example, let $f(x)=x^2$ as $x$ approach 4
The limit of $f(x)$: $\lim\limits_{x \to 4}x^2=16$
The derivative of $f(x)$ would be $(\frac{dx}{dy}x^2)_{x=4}=8$
The results are different which mean both limit and derivative are not the same. The derivative is not always the limit. The limit is not always the derivative.
