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# 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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- MichaelLv 41 decade agoFavorite Answer
(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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