The derivative of f(x, y) at p(1,2) in the direction of i+j is 2sqrt(2) and in the direction of -2j is -3. what is the derivative of f in the direction of -i-2j?

For the answer to the question above, well, let's imagine that the gradient off =(x,y) at P(1,2). Since that, we can found the hence using this way:  (x1,y1).(1,1)/ sqrt(2) with the result of : x1+y1 = 4
According to the 2nd directional derivative, we can have -2y1 = -6
Now it is not difficult to conclude that hence the gradient of f at (1,2) is (1,3) and we have to compute ( 1,3) and -1,-2) and divide it by the square root of five.
So, the answer that you will get in the end −(7/5√) I hope this helps