Consider the function $f(x)=\left\{\begin{aligned} x^2-5, & x \leq 3 \\ \sqrt{x+13}, & x \gt 3\end{aligned}\right.$ What is the differential coefficient of $f(x)$ at $x=12$ ?

• A

  $\frac{5}{2}$
• B

  5
• C

  $\frac{1}{5}$
• Correct answer
  D

  $\frac{1}{10}$

Hence, the correct answer is option: 'D'.