For the directional derivative there is a standard formula in terms of the dot product.
Directional derivative - Wikipedia, the free encyclopedia
For this we do grad(f) . v_hat (v_hat = i + j normalized)
So you have to relate grad(f) . z_hat (z_hat = i + j - k) to grad(f) . v_hat but you know the norm of grad(f) . v_hat so using these relationships you should get the answer.