Question

Show that the partial deriviatives of third and higher orders of f(x,y)-x^2+2xy^2-y^3 are constants.

Answer 1

f(x,y)=
not f(x,y)-

sry about that

Answer 2

the highest order for both x and y variable is degree two. so when you take the third or higher derivative you will only have a constant.
For Example
f(x)=x^2 zeroth derivative
f'(x)= 2x first derivative
f''(x)=2 Second derivative
f'''(x)=0 Third derivative