This week it was really just a review of chapter 2 something we learned how to do in chapter 2 was use the product rule and the quotient rule. You use the product rule when something is being multiplied and the quotient rule when something is being divided. We also reviewed how to use the identities that we learned from last year to help us get the simplified answer.
Product Rule:f(x)g(x) = f(x)g’(x) + g(x)f’(x)(recopy 1st)(derivative 2nd) + (recopy 2nd)(derivative 1st)Example: g(x) = (x^2 + 3)(x^2 – 4x)g’(x) = (x^2 + 3)(2x – 4) + (x^2 – 4x)(2x)= 2x^3 – 12 +2x^3 – 8x^2= 4x^3 – 8x^2 – 12 / 4= x^3 -2x^2 -3
Quotient Rule:f(x)/g(x) = g(x)f’(x) – [f(x)g’(x)] / (g(x))^2(recopy bottom)(derivative top) – [(recopy top)(derivative bottom)] / (bottom)^2Example: f(x) = x / x^2 + 1f’(x) = (x^2 + 1)(1) – [(x)(2x)] / (x^2+1)^2= x^2 + 1 – 2x^2 / (x^2 + 1)^2= -x^2 + 1 / (x^2 + 1)^2. We also learned how to find derivatives and the average velocity of something. That was chapter 2.