Chapter 14.5, Problem 2E

To determine

(a)

Tocalculate:

$\nabla f$ and $r\text{'}\left(t\right)$

To determine

(b)

Tocalculate:

$\frac{d}{dt}f\left(r\left(t\right)\right)$ by using the chain rule for path.

To determine

(c)

Towrite:

the composite $f\left(r\left(t\right)\right)$ as a function of $t$ and then differentiate. Check that the result agrees with part (b)