Reflection

This week in class we learned section two three: how to 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