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my homework question is what is the derivative of:

[(a + t * b) x (a + t * b + t^(2) * c)]

a, b, and c are vectors, and t is a constant. * is multipy, ^(2) is squared, and x is cross product.

i've been working on it for hours and i have no idea what to do.

there's another similar problem which i have the answer to. it asks to find the derivative of:

[(a + t * b) x (c + t * d)]

it has the same specs, with d being another vector.

the answer to this one is:

(a x d) + (b x c) + 2t(b x d)

i just don't see how these connect and can actually be equivalent.

help would be ridiculously appreciated.