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### Section 3-4 : Product and Quotient Rule

1. Use the Product Rule to find the derivative of $$f\left( t \right) = \left( {4{t^2} - t} \right)\left( {{t^3} - 8{t^2} + 12} \right)$$ .

Show Solution

There isn’t much to do here other than take the derivative using the product rule.

$f'\left( t \right) = \left( {8t - 1} \right)\left( {{t^3} - 8{t^2} + 12} \right) + \left( {4{t^2} - t} \right)\left( {3{t^2} - 16t} \right) = 20{t^4} - 132{t^3} + 24{t^2} + 96t - 12$

Note that we multiplied everything out to get a “simpler” answer.