Directional Derivative in the direction of steepest descent.

Hi

I just want to check that I am solving this correctly.

You are given a function and asked to find the directional derivative at the point in the **direction of the steepest descent**.

Partial Derivatives at :

Now this gives you the direction of the steepest descent : .

So you then find the unit vector:

And then you dot product the above with with the partial derivatives giving:

Is that the directional derivative? Or do I then have to substitute in the point ?

I would appreciate if someone could verify the above for me, or correct it (more likely!).

Also, is the magnitude of the rate of steepest descent ?

Thanks a lot.