10.6.3 Analytic functions

Problem: Prove that function $f(z)=u(x,y)+iv(x,y)$ is differentiable on the entire complex plane and find its derivative $f^{\prime }(z)$. $$\begin{array}{l}f(z)=(3x^3-6x{y}^2+2x^2-2y^2-3x+1)+\\ +i(6x^{2}y-2y^3+4xy-3y).\end{array}$$