Deriving the Product Rule for Derivatives Using Logarithmic Differentiation - Calculus

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This video uses logarithmic differentiation to derive the product rule that is used in calculus to take the derivative of a function that is the product of two other functions.

  1. James Elliott
  2. calculus
  3. AP Calculus
  4. derivative
  5. product rule
  6. logarithmic differentiation
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A Mr. Malama wants to sell cheese. After a fixed set-up cost of k250, he can produce the cheese at a cost of k9 per kilogram. He is able to produce up to 400 kg, but he plans to take advance orders and produce only what he can sell. His market research suggests that the amount he would be able to sell depends on the price in the following way: the amount decreases proportionally with the price; if he charged k20 per kg he would not sell any, and if the cheese was free he would ‘sell’ the maximum 400 kg that he could produce. What price per kilogram should the farmer set in order to maximize his profit?

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