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

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Answer 1 · 2017-05-09T03:45:12

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

$f(t) = t^2sint$

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

$= t^2cost+2tsint$

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