(1)The following rules were established as a part of algebra of derivatives:
(u ± v)′ = u′ ± v′
(2)
(uv)′ = u′v + uv′ (Leibnitz or product rule)
(3)
2
u
u v
uv
v
v
′
′ −
′

 =




, wherever v ≠ 0 (Quotient rule) The following table gives a list of derivatives of certain standard functions:
Table 5 3
Whenever we defined derivative, we had put a caution provided the limit exists Now the natural question is; what if it doesn’t