Multivariable Differential Calculus [cracked] Site

( \nabla f(\mathbfx) = \mathbf0 ).

The limit must be the same along all paths to ( \mathbfa ). If two paths give different limits, the limit does not exist. multivariable differential calculus

Existence of all partial derivatives does not guarantee differentiability (continuity of partials does). 7. The Gradient [ \nabla f(\mathbfx) = \left( \frac\partial f\partial x_1, \dots, \frac\partial f\partial x_n \right) ] ( \nabla f(\mathbfx) = \mathbf0 )