1. The problem statement, all variables and given/known data Let g(z) be an analytic function. I have to show that g'(z) is also analytic, using only the CR eqns. I am given that the 2nd partials are continuous 2. Relevant equations let f(x,y)=u(x,y)+iv(x,y) CR: du/dx=dv/dy and du/dy=-dv/dx continuous 2nd partials: d/dx(du/dy)=d/dy(du/dx) and d/dx(dv/dy)=d/dy(dv/dx) 3. The attempt at a solution I am confused as to how to express the derivative df/dz. would f'=du/dx+du/dy+idv/dx+idv/dy?