1. The original function is $v = \sqrt{4x^2 - 1}$. 2. You found the derivative $v' = 4x(4x^2 - 1)^{-1/2}$. 3. To use this derivative in the original question, simply replace $v'$ with $4x(4x^2 - 1)^{-1/2}$ wherever $v'$ appears. 4. This derivative represents the rate of change of $v$ with respect to $x$. 5. If the original question involves further operations with $v'$, proceed by substituting and simplifying using this expression. 6. Always remember to keep the expression in simplest form and apply algebraic rules carefully.