What is the directional derivative of the mountain at point P towards the peak?

[NewtonianAlch]

Homework Statement

A bush-walker is climbing a mountain, of which the equation is h \left( x,y \right) =400-{\frac {1}{10000}}\,{x}^{2}-{\frac {1}{2500}<br /> }\,{y}^{2}<br />

The x-axis points East, and the y-axis points North. The bush-walker is at a point P, 1600 metres West, and 400 metres South of the peak.

What is the slope of the mountain at P in the direction of the peak?

The Attempt at a Solution

I'm fairly sure on how to solve this, except I need a few different elements. Since we have the starting point, I can calculate the gradient at that point. I need to find a directional vector (to the peak) from that point, and that's what I'm not sure to find.

Looking at the equation for the mountain, I'm guessing its peak is when (x,y) = (0,0)

I first tried for v = +1600i + 400j, but that was not correct.

The answer 8/5*sqrt(17) = 0.388

 

[NewtonianAlch]

NVM, I figured it out. I was mistakenly keeping the 400 as part of the equation whilst calculating the gradient.