Ok, so I kept getting an Latex Error:Unknown Error when I tried to enter my stuff in LaTex. Then I scanned my handwritten work and tried to attach it...it just timed out on me everytime. Sorry this is so primitive, but I just typed everything out. I'm looking for someone to check my work and help me with the last part of #20. Here are the two problems:

19. Suppose that z=e^{xy+x-y}. How fast is z changing when we move away from the origin toward (2,1)?

20. In problem 19 in what direction should we move away from the origin for z to change most rapidly? What is the maximum rate of change? In what directions is the derivative zero at the origin?

Here is my work:

19.z=e^{xy+x-y}

P=(0,0)

v=<2,1>

u={1/sqrt(5)}<2,1>

DZ/DX=(y+1)*e^{xy+x-y}

DZ/DY=(x-1)e^{xy+x-y}

DZ/DX(0,0)=1

DZ/DY(0,0)=-1

Gradient of z(0,0)=<1,-1>

Directional Derivative of z at (0,0)=<1,-1> . (1/sqrt{5})<2,1>=(1/sqrt{5})

Answer to 19: (1/sqrt{5})

20. The gradient of z(0,0)=<1,-1> is the direction we should move away from (0,0) for z to change most rapidly.

The maximum rate is sqrt{2}

-I'm stuck on the last part of question 20: "In what directions is the derivative zero at the origin?" Can someone help me with this part? Thanks.