Differentiation Rules
Differentiation rules are rules (actually, theorems) used to compute the derivative of a function in calculus. In what follows, all functions are assumed to be differentiable.
Basic Rules
Derivative of a Constant:
If is a constant function then
.
Sum Rule:
If then
.
Product Rule:
If then
.
Quotient Rule:
If then
.
Chain Rule:
If then
.
Power Rule:
If then
. For integer
this is just a consequence of the product and quotient rules and induction, but it can also be proven for all real numbers
, e.g. by using the extended Binomial Theorem.