Which of the following is the correct expression of instantaneous acceleration?

• A. \[a=\frac{\Delta v}{{{(\Delta t)}^{2}}}\]
• B. \[a=\frac{dv}{dt}\]
• C. \[a=\frac{{{d}^{2}}v}{d{{t}^{2}}}\]
• D. \[a={{\left( \frac{\Delta v}{\Delta t} \right)}^{2}}\]