What is the derivative of:
$\displaystyle
t^{2} sin bt
$
Would that be the product Rule or the Chain Rule?
A bit of both:
$\displaystyle f(t) = t^2 \cdot sin(bt)$
$\displaystyle f^{\prime}(t) = (t^2)^{\prime} \cdot sin(bt) + (t^2) \cdot (sin(bt))^{\prime}$
$\displaystyle f^{\prime}(t) = 2t \cdot sin(bt) + (t^2) \cdot cos(bt) \cdot b$
$\displaystyle f^{\prime}(t) = 2t \cdot sin(bt) + bt^2 \cdot cos(bt)$
-Dan