function of two variables, directional derivatives

Let f(x,y) be a function that is differtiable everywhere. At a certain point P in the xy plane, the directional derivative of F in the direction of i - j is sqrt(2) and the directional derivative of f in the direction of i + j is 3sqrt(2). What is the maximum directional derivative at P?

A) 3sqrt(2) B) 2sqrt(5) C) 43sqrt(5) D) 6 E) 8

I know the directional derivative is the del of f(x,y) = <fx, fy>. I also know that the directional derivative also points in the direction of maximum increase.

So should i have <fx, fy> = i - j meaning fx = 1 and fy = -1 evaluated at P?

Same for <fx, fy> = i + j meaning fx = 1 and fy = 1 at P?

I am not sure what to do can someone help me out