Directional Derivatives and the Gradient Vector: Examples


1. Find the gradient for the following equation:
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Answer:

Find both $f_{x}$ and $f_{y}$ for the function:
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2. Find the derivative of the above function in the direction <2,3>.

Answer:

The directional derivative is the dot product of the gradient and the unit vector of the direction of travel.

First, find the unit vector <2,3>
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The directional derivative is then:
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