Answer to Question #259231 in Calculus for emmanuelokoye002@g

Question #259231

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


1
Expert's answer
2021-11-01T16:19:38-0400

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


(fg)(t)=(4t²itj+t²k)(ti+2t²j+4(sint)k)(fg)(t) = (4t²i-tj+t²k)(ti+2t²j+4(sint)k)

(fg)(t)=4t³2t³+4t²(sint)(fg)(t) = 4t³-2t³+4t²(sint)

(fg)(t)=2t³+4t²(sint)(fg)(t)=2t³+4t²(sint)


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





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