Editing Directional derivative (section)

== Properties ==
Many of the familiar properties of the ordinary [[derivative]] hold for the directional derivative.  These include, for any functions ''f'' and ''g'' defined in a [[neighborhood (mathematics)|neighborhood]] of, and [[total derivative|differentiable]] at, '''p''': 

# '''[[Sum rule in differentiation|sum rule]]''': <math display="block">\nabla_{\mathbf{v}} (f + g) = \nabla_{\mathbf{v}} f + \nabla_{\mathbf{v}} g.</math>
# '''[[Constant factor rule in differentiation|constant factor rule]]''': For any constant ''c'', <math display="block">\nabla_{\mathbf{v}} (cf) = c\nabla_{\mathbf{v}} f.</math>
# '''[[product rule]]''' (or '''Leibniz's rule'''): <math display="block">\nabla_{\mathbf{v}} (fg) = g\nabla_{\mathbf{v}} f + f\nabla_{\mathbf{v}} g.</math>
# '''[[chain rule]]''': If ''g'' is differentiable at '''p''' and ''h'' is differentiable at ''g''('''p'''), then <math display="block">\nabla_{\mathbf{v}}(h\circ g)(\mathbf{p}) = h'(g(\mathbf{p})) \nabla_{\mathbf{v}} g (\mathbf{p}).</math>