Compute the directional derivative of the following function at the given point P in the direction of the given vector. Be sure to use a unit vector for the direction vector. f(x, y)= ln(2 +3x^2 +3y^2); P(1,-2); (3,1)

The directional derivate is given by:

Step-by-step explanation:

The directional derivative at point (x,y) is given by:

In which a is the x component of the unit vector and b is the y component of the unit vector.

Vector:

We are given the following vector:

Its modulus is given by:

The unit vector is given by each component divided by it's modulus. So

This means that

Partial derivatives:

So

Directional derivative:

The directional derivate is given by:

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step-by-step explanation: