The line that passes through the point and that has direction is given vectorially by . Hence, the line is given by
or parametrically, by . Note that this parametrization puts the line at when .
The function along this line reduces to
The rate of change of at the given point is , computed as follows. First obtain
then evaluate at to obtain
The vector arises naturally via the chain rule. The differential operator
is called the nabla or del operator, and the vector is called the gradient of .
