Modul
e 3
: Differentiation and Mean Value Theorems
Lecture
8 : Chain Rule [Section 8.1]
8.1.14
Note
It may not be always possible to represent explicitly
as a function of
.
Practice Exercise 8.2 : Chain rule and applications
1.
Compute
for the following functions wherever they are defined:
(i)
.
(ii)
.
(iii)
.
2.
Let
be differentiable functions such that
. Given that,
, compute.
.
3.
Let
be expressible in terms of
by the relation
. Find the largest interval of the form
such that
will be differentiable as a function of
.
1
2
3
4
5
6
7
8
9
10
11
12
13
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20
as a function of 
. 
for the following functions wherever they are defined: 
.
.
. 
be differentiable functions such that 
. Given that, 
, compute. 
. 
be expressible in terms of 
by the relation 
. Find the largest interval of the form 
such that 
will be differentiable as a function of 
. 
