"You are standing at the point (30, 20, 5) on a hill with the shape of the surface z=100exp((-x^2+3y^2)/701). In what direction should you proceed in order to climb most steeply?"

SInce the grad vector allegedly points in the most steep direction of the surface, I guess I'll have to compute that one. But I'm not sure if I'm suppoesd to compute the partials of all of x, y and z or only x and y in the gradient. How can I know that?

Edit: z is a function of x and y.

the thing is, it depends on what kind of increase you want. obviously from the question, it implies the direction that z ("climb most steeply") increases most rapidly. so, take the derivatives with respect to z.

HallsofIvy