The directional derivative and the chain rule

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After completing this section, students should be able to do the following.

Compute directional derivatives.
Use the directional derivative to show that the gradient vector points in the initial direction of greatest increase for the function.
View the chain rule in terms of the gradient.
Compute the derivative of the composition of a function of several variables with a vector-valued function.
Use the chain rule of several variables to implicitly differentiate a curve.