Modul
e
11 : Partial derivatives, Chain rules, Implicit differentiation, Gradient, Directional derivatives
Lecture
32 : Chain rules [Section 32.1]
Practice Exercises
1.
Compute
and
where
(i)
(ii)
Answers
2.
If
is differentiable and
show that
3.
Let
be such that for some
and all
Show that if
is differentiable, then
1
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3
4
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7
8
9
10
11
12
and 
where 
is differentiable and 
be such that for some 
and all 
is differentiable, then 
