Question

1. Find the derivative of the following functions:

1. Y = 10X³ – 20X² + 10X -5
2. Y = 23X⁵ -120X²

   (10 points)

• Rules for taking derivatives are found on p. 103
• Most economic derivative equations can found using the first three rules so I will briefly note those.

1. Constant Rule – any term that does not include a variable does not vary and has a derivative of zero
2. Power Function Rule – reduce the exponent of the variable by one power, and multiply the original power times the function
3. Sum/Difference Rule – basically it means you take the derivative of each term (function) in the equation and you have the derivative equation.

• Derivative equations are equations that measure the rate of change in an initial equation. The most common use of them in Economics to find a marginal equation from a total equation since marginal revenue, cost, utility, etc. measure changes in total revenue, cost, utility, etc. When you find the derivative of TR you will be writing an equation for MR

Answer 1

a. The function is given as: Y = 10X³ – 20X² + 10X -5

The derivative of this function Y with respect to X is given by dY/dX

The result is:

Thus, dY/dX = 30X²  – 20X + 10

b. The function as given is: Y = 23X⁵ -120X²

The derivative dY/dX is given by:

Thus, dY/dX = 115X⁴ -120X