Question

How do you find the derivative of `f(t) = t² sin t`?

Answer 1

`f'(t) =t^2cost+2tsint`

Explanation:

`f(t) = t^2sint`

The Product rule states that:

If `f(t) = g(t)h(t)` then `f'(t) = g(t)h'(t)+ g'(t)h(t)`

In this example: `g(t) = t^2` and `h(t) = sint`

Hence, `f'(t) = t^2*d/dtsint + d/dt t^2 * sint`

`= t^2cost+2tsint`