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### Section 3.5 : Derivatives of Trig Functions

7. Differentiate $$h\left( t \right) = {t^3} - {t^2}\sin \left( t \right)$$ .

Show Solution

Not much to do here other than take the derivative, which will require the product rule for the second term.

You’ll need to be careful with the minus sign on the second term. You can either use a set of parentheses around the derivative of the second term or you can think of the minus sign as part of the “first” function. We’ll think of the minus sign as part of the first function for this problem.

$\require{bbox} \bbox[2pt,border:1px solid black]{{h'\left( t \right) = 3{t^2} - 2t\sin \left( t \right) - {t^2}\cos \left( t \right)}}$