Module 3 : Differentiation and Mean Value Theorems
Lecture 8 : Chain Rule [Section 8.1]
8.1
Chain Rule
In the previous section we analysed the differentiability of algebraic combinations of differentiable functions. In this section we analyse the differentiability of the composition of differentiable functions.
8.1.1
Theorem (Chain Rule):
Let and be functions such that is defined. If is differentiable at and is differentiable at , then is differentiable at and
Alternatively, if
then,
.
Click here to View the Interactive animation : Applet 8.1
and 
be functions such that 
is defined. If 
is differentiable at 
and 
is differentiable at 
, then 
is differentiable at 
and 
. 
Then 
