# Lesson Worksheet: Directional Derivatives and Gradient Mathematics

In this worksheet, we will practice finding a derivative of multivariable functions in a given direction (directional derivative) and finding the gradient vector of the function.

**Q1: **

Find a function so that the vector field is a gradient field.

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**Q2: **

Suppose with . Express the gradient (viewed as a matrix) in terms of the matrix , where , and a matrix of partial derivatives of .

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**Q3: **

Suppose with and that for a point . Express the gradient (viewed as a matrix) in terms of the matrix and a matrix of partial derivatives of .

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**Q4: **

Let where and . Given that there is a line in the - plane for which , find the equation of this line.

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