Question

For the function , find the directional derivative at (5, 2) in the direction.

Answer 1

The function is not specified, so it is not possible to calculate the directional derivative at the point
`((5,2))` in the direction of a vector without knowing the function. If the function is provided, the directional derivative can be calculated using the formula above.

Explanation:

The directional derivative of a function at a point in the direction of a vector is a measure of the rate of change of the function in that direction. It is calculated using the gradient of the function and the unit vector in the direction of the vector.

The formula for the directional derivative is:

`[ D_{\vec{u}}f(a,b) = \\abla f(a,b) \cdot \vec{u} ]`

where
`( \\abla f(a,b) )` is the gradient of the function at the point
`((a,b)) and ( \vec{u} )` is the unit vector in the direction of the vector.

In the given question, the function is not specified, so it is not possible to calculate the directional derivative at the point
`((5,2))` in the direction of a vector without knowing the function. If the function is provided, the directional derivative can be calculated using the formula above.