Question

Which of the following equations hold for all differentiable vector functions u(t), v(t) and all differentiable scalar functions f(t)? A: $(u(t)\cdot v(t))' = u'(t)\cdot v(t) + u(t)\cdot v'(t)$, B: $(u(t)\times v(t))' = u'(t)\times v(t) + u(t)\times v'(t)$, C: $(f(t)u(t))' = f'(t)u'(t) + f(t)u(t)$.

          Which of the following equations hold for all differentiable vector functions u(t), v(t) and all differentiable scalar functions f(t)?
A:
$(u(t)\cdot v(t))' = u'(t)\cdot v(t) + u(t)\cdot v'(t)$, 
B:
$(u(t)\times v(t))' = u'(t)\times v(t) + u(t)\times v'(t)$, 
C:
$(f(t)u(t))' = f'(t)u'(t) + f(t)u(t)$.

Which of the following equations hold for all differentiable vector functions u(t), v(t) and all differentiable scalar functions f(t)?
A:
(u(t)· v(t))' = u'(t)· v(t) + u(t)· v'(t),
B:
(u(t)× v(t))' = u'(t)× v(t) + u(t)× v'(t),
C:
(f(t)u(t))' = f'(t)u'(t) + f(t)u(t).

Added by Christopher M.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Supreeta N

05/07/2023

Step 1

This rule applies to scalar functions, vector functions, and their products. Show more…

Show all steps

Thanks for your feedback!

Which of the following equations hold for all differentiable vector functions u(t), v(t), and all differentiable scalar functions f(t)? A: (u(t)*v(t))' = u'(t)*v(t) + u(t)*v'(t) B: (u(t) x v(t))' = u'(t) x v(t) + u(t) x v'(t) C: (f(t)u(t))' = f'(t)u'(t) + f(t)u(t) Which of the following equations hold for all differentiable vector functions u(t), v(t), and all differentiable scalar functions f(t)? A: u(t)v(t) = u(t)v(t) + u(t) - v(t) B: u(t) x v(t) = u(t) x v(t) + u(t) x v'(t) C: f(t)u(t)' = f'(t)u'(t) + f(t)u(t)