Warning:That Tutorvista page is complete gibberish from start to finish. Do not be misled by it.

If you have a differentiable function of a complex variable, in the form f(z) = u(x,y) + iv(x,y) (where z = x+iy, of course), then its derivative is given by the formula

That formula may look odd, because why should you differentiate both functions u(x,y) and v(x,y) partially with respect to x, and not with respect to y? The answer is that you could equally well differentiate both functions with respect to iy, and you would get the same answer for f'(z) as in the above formula, because of the Cauchy–Riemann equations.