Answer
r'(t)= a x (b + 2tc)
Work Step by Step
r(t)= ta x (b + tc)
Using the product rule:
r'(t) = (ta)' x (b + tc) + ta x (b + tc)'
product rule again and further simplification:
r'(t) = (a + a't) x (b + tc) + ta x (b' + (c + tc'))
because a, b and c are constant vectors, their derivatives are 0, and the derivative becomes:
r'(t) = a x (b + tc) + ta x c
Which can be rewritten as:
r'(t) = a x (b + tc) + a x tc
r'(t)= a x (b + 2tc)
