In this worksheet, we will practice finding the directional derivative and the gradient vector of nice functions in 2 or 3 variables.

**Q1: **

Find the directional derivative of at the point in the direction of .

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**Q2: **

Find the directional derivative of at the point in the direction of .

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**Q3: **

Find the directional derivative of at the point in the direction of .

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**Q4: **

Find the directional derivative of at the point in the direction of .

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**Q5: **

Find the directional derivative of at the point in the direction of .

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**Q6: **

Find the directional derivative of at the point in the direction of .

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**Q7: **

Compute the gradient of .

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**Q8: **

The temperature of a solid is given by the function , where , , are space coordinates relative to the centre of the solid. In which direction from the point will the temperature decrease the fastest?

- A decreases the fastest in the direction of .
- B decreases the fastest in the direction of .
- C decreases the fastest in the direction of .
- D decreases the fastest in the direction of .

**Q9: **

In which direction does the function increases the fastest from the point ? In which direction does it decrease the fastest? Give your answer using unit vectors.

- A increases the fastest in the direction of and decreases the fastest in the direction of .
- B increases the fastest in the direction of and decreases the fastest in the direction of .
- C increases the fastest in the direction of and decreases the fastest in the direction of .
- D increases the fastest in the direction of and decreases the fastest in the direction of .