




Given a scalar field f, its gradient is a vector normal to the surface on which
the field is constant, of length given by f's directional derivative in that
direction.
We can always write
df
or , after trivial manipulation,
We may identify ds_{j }= u_{j}dw_{j }, and obtain
Suppose we set two of the ds_{i}'s to zero; then the directional derivative of f in the third direction must be the component of the gradient in that direction. We therefore obtain