Vi beräknar först de partiella derivatorna: \[ \frac{\partial f}{\partial x}=\cos(x+y)-x\sin(x+y), \quad \frac{\partial f}{\partial y}=-x\sin(x+y)+1, \] vilket ger att \[ f(\pi,0)=-\pi, \quad \frac{\partial f}{\partial x}(\pi,0)=-1, \quad \frac{\partial f}{\partial y}(\pi,0)=1. \] Insatt i tangentplanets ekvation får vi \[ z=-\pi +(-1)\cdot(x-\pi)+1\cdot y\Leftrightarrow z=-x+y. \]