Chapter 2 Handouts What is a derivative

I want to reiterate however you will not need to use

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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(b-1) Example #1: Example #2: Example #3: Example #4: y = 2x so dy/dx = 2 * x(1-1) = 2x0 = 2 3 so dy/dx = 4 * 3 * x(3-1) = 12x2 y = 4x 2 TR = 10Q – Q so dTR/dQ = 10(Q) (1-1) - 2(Q) (2-1) = 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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