Question

If F(t) = 4t^2i - tj + t^2k and G(t) = ti + 2t^2j + 4 sin t k, then find d/dt (F*G)

Answer 1

We shall determine F*G first then evaluate $\frac{d((fg)(t))}{dt}$

$(fg)(t) = (4t²i-tj+t²k)(ti+2t²j+4(sint)k)$

$(fg)(t) = 4t³-2t³+4t²(sint)$

$(fg)(t)=2t³+4t²(sint)$

$=> \frac{d((fg)(t))}{dt}=6t²+8t(sint)+4t²(cost)$