def provideJ(self):

        df_dx = 2.0*self.x - 6.0 + self.y
        df_dy = 2.0*self.y + 8.0 + self.x

        self.J = array([[df_dx, df_dy]])
        return self.J
Analytical first derivatives
dataset/ETHPy150Open OpenMDAO/OpenMDAO-Framework/openmdao.main/src/openmdao/main/test/test_system.py/Paraboloid.provideJ