Question

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?

Answer 1

Well, lets imagine that the gradient of f =$(x1,y1) at (1,2)$
Since that, we can found the hence using this way : $(x1,y1) . (1,1)/sqrt(2) = 2 sqrt(2)$ with the result of : $x1+y1 = 4$
According to the 2nd directional derivative we can have $-2 y1 =-6$
Now it is not difficult to conclude that hence the gradient of f at (1,2) is (1,3) and we have to compute $(1,3) . (-1,-2)$ and divide by sqrt(5). 
Finally, here is the answer that you will get in the end −(7/5√)