If F(t) = 4t^2i - tj + t^2k and G(t) = ti + 2t^2j + 4 sin t k, then find d/dt (F*G)
We shall determine F*G first then evaluate d((fg)(t))dt\frac{d((fg)(t))}{dt}dtd((fg)(t))
(fg)(t)=(4t²i−tj+t²k)(ti+2t²j+4(sint)k)(fg)(t) = (4t²i-tj+t²k)(ti+2t²j+4(sint)k)(fg)(t)=(4t²i−tj+t²k)(ti+2t²j+4(sint)k)
(fg)(t)=4t³−2t³+4t²(sint)(fg)(t) = 4t³-2t³+4t²(sint)(fg)(t)=4t³−2t³+4t²(sint)
(fg)(t)=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)=>dtd((fg)(t))=6t²+8t(sint)+4t²(cost)
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