**Differentiation of a Vector**

Let V^{→} (u) be a vector that depends on unit scalar operator u. In mathematical language V is a function of u. Then we can write,

∆R^{→}/∆u = [∆R(u+∆u) – R (u)] / ∆u

here ∆u, means a small increases of u.

∆R^{→}/∆u is the rate of change of R^{→} with respect to u. When ∆u tends to zero,

lim_{∆u→0} ∆R^{→}/∆u = lim_{∆u→0} [∆R(u+∆u) – R (u)] / ∆u

lim_{∆u→0} ∆R^{→}/∆u can be written as dR^{→}/du.

So, lim_{∆u→0} ∆R^{→}/∆u = dR^{→}/du = lim_{∆u→0} = [∆R(u+∆u) – R (u)] / ∆u

dR^{→}/du; means the rate of change of R^{→} with respect to u for exceedingly small change of u.

dR^{→}/du; called the differential coefficient of R^{→} with respect to u.

**Process of determining dR ^{→}/du is called differentiation.**