1. Managerial Economics Session 1: General Concept of Calculus for Microeconomics
Instructor Samir Sharma
Room No. 303

2. Evaluation Criteria Attendance 5% Class Participation and quizzes 10%
Presentation %
Internal Term exam 30% (End Term)
Class Tests/ Mid Term 20% (Tests)
Assignments % (2 Assignts.)

3. 3 Very Important Rules: Never Forget!
Assignments:
No copy. All of you would get zero if found copied regardless of who copied whom.
Strictly adhere to the due date. No assignments will be accepted after the due date.
Class Tests:
There will be no re-test. You will not get grades if you miss it.
Group Presentation:
All members should make presentation. Every one should be present on the day of presentation.

4. What are/ is your expectation/s from this course?

5. General Concept of Calculus for Microeconomics-Reminder

6. Meaning of Slopes x1 x2

7. Meaning of Slopes
Example of Slopes

8. Slopes of a Curve How to calculate the slope of a curve whose slopes
changes at every points?
For example: a parabola : y = x2

9. Use of Secant and Tangent Lines
Secant Line:

10. Finding slope of the Tangent line-The Derivative
The Derivative or Slope of the Tangent Line at a Curve:
f (xo
+ h ) – f (
Xo) =
= f ‘ x xo + - xo h

11. Examples using Derivatives
Find the equation of the tangent line to the graph of f (x) = x2 at x = 3.
SOLUTION
(3+h)2 - 9
Slope =
3+h - 3
9 +6h+h2 -9
(3+h),(3+h)2 = h
(3+h)2
= 6+h
(3, 9)
Lim h->0 9
(6+h) = 6 3
(3+h)

12. Differentiation Examples (Rules)
Rule 1. Power Rules for Positive Integer
This is the given equation.
EXAMPLE 1
Find the derivative of
SOLUTION = =
EXAMPLE 2
Find the slope of curve y = x5 at x the = -2. = = =
Therefore, the slope of the original function at x = -2 is 80 (or 80/1).

13. Differentiation Examples (Rules)
Rule I1. Differential Sum Rule
EXAMPLE 1
Find the derivatives of y = x7+x3 at x = 2 dy d d d =
(x7+x3) =
(x7 ) + =
7x7-1+3x3-1 =
7x6+3x2
(x3) dx dx dx dx
Lim x->2
(7x6+3x2) = = 460

14. Differentiation Examples (Rules)
Rule III. Product Rule
EXAMPLE 1
Find the derivatives of x2(x3+1)
Here u = x2 and v = x3+1

15. Differentiation Examples (Rules)
Rule IV Quotient Rule
x2-1
EXAMPLE 1
Find the derivatives of x
Here u = x2-1 and v = x

16. Differentiation Examples (Rules)
Rule VI Chain Rule
EXAMPLE 1
Find the derivatives of
y = u4
and u = x2-x+3
Here y is the function of u and u is the function of x
Find derivatives for first and second function simultaneously and multiply them.

17. Parametric Functions
Parametric functions are those functions in which both x and y and expressed in terms of other variables called parameter.
For example: x = f(t) and y = g(t)
Rules for differentiation: dy dy dt = dx dx dt

18. Implicit Functions
Sometimes x and y are expressed both sides of the equations
For example; x+y = xy or axy
For example: x = f(t) and y = g(t)
Rules for differentiation: X3 y3 = dy
Solve each side of equation with respect to x
Solve for f’(x)

19. Higher Order Derivatives
First derivatives of y with respect to x :
Differentiating the first derivative with respect to x again, we get Second Deriative of y with respect to x :
Rules for differentiation:
Solve for first derivative
For reminder solve again with respect to x dy dx
d2y
dx2

20. Thank you