Lecture 5, Unit 4: Differentiation (continued)
18/2/2015
Outline
1
Introduction
2
Examples
3
Economic Applications: MR and MC
4
Conclusion
Literature
Renshaw, ch. 6 & ch. 13 (13.213.3)
Introduction
•
Last time we encountered the rules of differentiation
•
Today we’ll apply these rules to find the derivatives of some
functions
•
We’ll also introduce the marginal revenue and marginal cost
functions
Example 1
•
Suppose that
y
= (4
x
2

3)(2
x
5
+
x
).
•
Find
dy
dx
Example 2
•
Suppose that
y
=
x
2
+1
1

x
2
.
•
Find
dy
dx
Example 3
•
Suppose that
y
= (
x
2

2
x
3
)
5
.
•
Find
dy
dx
Example 4
•
Suppose that
y
=
1
√
e
x
.
•
Find
dy
dx
Example 5
•
Suppose that
y
= ln
1
√
x
.
•
Find
dy
dx
Economic Applications
•
Two frequently encountered applications derivatives are:
•
Marginal revenue function
•
Marginal cost function
Marginal revenue, MR: p. 233
•
Recall that total revenue is
R
=
pq
We often have to multiply demand curve/function by p
(alternatively, multiply inverse demand curve/function by q)
to obtain total revenue function
•
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