This week in class we learned how to use the product rule and the quotient rule. You use the product rule when you are using multiplication. You use the quotient rule when when you are doing division.
-Product Rule:
f(x)g(x) = f(x)g’(x) + g(x)f’(x)(copy 1st)(derivative 2nd) + (copy 2nd)(derivative 1st)
Ex. g(x)= (3x^2+4)(2x^2-3x)
=(3x^2+4)(4x-3)-(2x^2-3x)(6x)
=12x^3-9x^2+16x-12-12x^3+9x^2
=16x-2
-Quotient Rule:
f(x)/g(x) = g(x)f’(x) – [f(x)g’(x)] / (g(x))^2(copy bottom)(derivative top) – [(copy top)(derivative bottom)] / (bottom)^2
You solve the same way with the quotient rule, following the steps (formula) and when simplifying, if there is a trig identity in the answer use the identity to simplify the answer completely.
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