Quotient rule for differentiation
This article is about a differentiation rule, i.e., a rule for differentiating a function expressed in terms of other functions whose derivatives are known.
View other differentiation rules
Statement
Suppose and
are functions defined at and around a point
and they are both differentiable at
(i.e., the derivatives
and
are defined) and
. Then, the quotient
is differentiable at
, and its derivative is given as follows:
If we consider the general expressions rather than the evaluation at a particular point , we can rewrite the above as:
Related rules
- Product rule for differentiation
- Second derivative rule for parametric descriptions (uses the quotient rule in its proof)
- Quotient rule for second derivative