To understand it better let us consider an example of a function that is given as::

F (v) = 10 v

^{7}– 41 v

^{6}+ 4 v

^{4}+ 15 v

^{2}+ 10 v

To differentiate this function we will follow the above mentioned formula and the general rules of differentiation. So, we can write the derivative with respect to the variable v as:

F

^{’}(v) = d (10 v

^{7}– 41 v

^{6}+ 4 v

^{4}+ 15 v

^{2}+ 10 v) / dv, differentiating each term in the function with respect to v:

F

^{’}(v) = d (10 v

^{7}) / dv – d (41 v

^{6}) / dv + d (4 v

^{4}) / dv+ d (15 v

^{2}) / dv+ d (10 v) / dv

As the differentiation of constant values results to zero we are left with:

F

^{’}(v) = 10 d (v

^{7}) / dv – 41 d (v

^{6}) / dv + 4 d (v

^{4}) / dv+ 15 d (v

^{2}) / dv+ 10 d (v) / dv

Using the formula we get:

F

^{’}(v) = (7 * 10 (v

^{7-1})) – (6 * 41 (v

^{6-1})) + (4 * 4 (v

^{4-1})) + (15 * 2 (v

^{2-1})) + (10 *1 (v

^{1-1}))

Or F

^{’}(v) = 70 v

^{6}– 246 v

^{5}+ 16 v

^{3}+ 30 v

^{1}+ 10 (First derivative)

In the similar way the other higher order derivatives can be finding easily.