The Complex Derivative at a Point and Analyticity

[stihl29]

Homework Statement

f(z) = xy + i(xy+x)

has a derivative at exactly one point after locating the point find the derivative there and give the numerical value is the function analytic at this point?

Homework Equations

My C-R equations are du/dx = y, dv/dy = x, dv/dx = y+1, du/dy = x

The Attempt at a Solution

i don't really know how to interpret the C-R equations.
answer is z = -1/2 - i/2 f ' = -1/2 + i/2 and not analytic

 

[lanedance]

CR actually means a relation satisfied by the partial derviatives for a complex function to be analytic (holomorphic)

you have only given the partial derivatives, do you know the CR equations?