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Unformatted text preview: variable. A partial derivative is used when you have a function
written in terms of multiple variables. I want to reiterate, however – you will not need to use calculus to
actually find derivatives in this class, but you should understand the two basic rules below so you
understand where they came from and how to use them. The book provides the equations for you. You
will, however, need to apply calculus to find maximums or minimums. This is explained more in the
handout on marginal analysis, which you should review next.
Several basic rules of differentiation you should be familiar with: 1. CONSTANT FUNCTION RULE
If Y = ƒ(X) = a where a = constant then dY/dX = y' = 0 Example: If y = 2, then dY/dX = 0 as “2” never changes, so the marginal change = 0 (i.e., the
derivative = 0)
Example: TR = $32. In this case, dTR/dQ = zero, since total revenue is always $32. It would
graph as a horizontal line at $32, and horizontal lines have no rate of change (i.e., their slope if
zero). 2 MBA 6651 Differentiation: What is It? Dr. Wendy Bailey 2. POWER FUNCTION RULE
If y = aXb, where a= constant and b= exponent (power), then dY/dX = b * a * X(b1)
Example #1:
Example #2:
Example #3:
Example #4: y = 2x
so dy/dx = 2 * x(11) = 2x0 = 2
3
so dy/dx = 4 * 3 * x(31) = 12x2
y = 4x
2
TR = 10Q – Q so dTR/dQ = 10(Q) (11)  2(Q) (21) = 10Q0  2Q1 = 10 – 2Q
TC = 100 + 2Q – 3Q2 so dTC/dQ = 0 + 2 + 3(2)Q = 2 + 6Q Some simple applications as more examples:
• The derivative a number is...
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 Fall '10
 BAILEY
 Economics

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