calc_tutorial_13_2_025

Question 1

Choose how to apply the Chain Rule to a differentiable vector-valued function r(t) and a differentiable --------scalar-valuedvector-valued function g(t).

A.

(d / dt)r(g(t)) = g'(t)r'(g(t))

B.

(d / dt)r(g(t)) = g(t)r'(g'(t))

C.

(d / dt)r(g(t)) = r(t)r'(g'(t))

Recall how to find the derivative of a vector-valued function. A vector-valued function r(t) = <x(t), y(t), z(t)> is differentiable if and only if each component is differentiable. The derivative is given as follows.

r'(t) = (d / dt)r(t) = <x'(t), y'(t), z'(t)>

Calculate r'(t) for

r'(t) =

A.

B.

C.

D.

Calculate g'(t) for g(t) = 3t + 5.

g'(t) =

Question 2

Use the Chain Rule to evaluate (d / dt)r(g(t)).

(d / dt)r(g(t)) = g'(t)r'(g(t)) =

A.

B.

C.

D.

=

A.

B.

C.

D.