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?

Well, lets imagine that the gradient of f =
Since that, we can found the hence using this way :  with the result of : 
According to the 2nd directional derivative we can have 
Now it is not difficult to conclude that hence the gradient of f at (1,2) is (1,3) and we have to compute  and divide by sqrt(5). 
Finally, here is the answer that you will get in the end −(7/5√)