find the derivative of the trigonometric function?

Question

t^2sint
i know the answer but i dont know how
the answer is t(tcost+2sint) HOW!!!!!!!!!!!!!!!!!!!

Answer 1

You should use the product rule
u = t^2 v= sin t
d/dt(uv) = u dv/dt + v du/dt
d/dt(t^2 sin t) = t^2 d/dt(sin t) + sin t (d/dt(t^2))

now d/dt(sin t) = cos t

and d/dt(t^2) using the formula d/dt(t^n) = nt^(n-1)
is 2t
so
d/dt(t^2 sin t) = t^2 cos t + 2t sin t
= t(t cos t+ 2 sint)
proved

Answer 2

d/dt(t^2sint)
2tsint+t^2(cost)
t(tcost+2sint)

Answer 3

f (t) = (t ²) (sin t)
f `(t) = ( 2 t ) ( sin t ) + ( cos t ) ( t ² )
f `(t) = t ( 2 sin t + t cos t )