haha
Lv 7
haha asked in 科學數學 · 1 decade ago

carrying out the vector operat

compute the requested derivative

(a)by carrying out the vectoroperation and differenting the resulting vector or scalar, and (b) byusing one of the differentiation rules.

F(t)=-9i+(t^2)j+(t^2)k

G(t)=(e^t)i

(d/dt)[F(t)xG(t)]

x==cross

1 Answer

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  • 1 decade ago
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    (a)

    (d/dt)[F(t)xG(t)] = (d/dt) [ (t^2*e^t)*j - (t^2*e^t)*k] = (2t + t^2)*e^t*j + (-2t - t^2) *e^t *k

    (b)

    (d/dt)[F(t)xG(t)] = F'(t)xG(t) + F(t)xG'(t) = (0, 2t, 2t) x (e^t, 0, 0) + (-9, t^2, t^2) x (e^t, 0, 0) = (0, 2t*e^t, -2t*e^t) + (0, t^2*e^t, -t^2*e^t) = (0, (2t+t^2)*e^t, (-2t-t^2)*e^t)

    Source(s): me
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