Module 3 : Differentiation and Mean Value Theorems
Lecture 8 : Chain Rule [Section 8.1]
8.1.6
Parametric Differentiation:
Consider a curve in the plane which is the graph of a function . Suppose that both the variables and are functions of another variable , say, and Then, the function is called a parametric representation of the curve .
Further, suppose that is differentiable as a function of and is differentiable as a function of . Then by the chain rule, the function is differentiable as a function of and
in the plane 
which is the graph of a function 
. Suppose that both the variables 
and 
are functions of another variable 
, say, 
and 
Then, the function 
is called a 
. 
is differentiable as a function of 
and 
is differentiable as a function of 
. Then by the chain rule, the function 
is differentiable as a function of 
and 
, we can write 
