to 
specified by m functions,
of n variables.
Recall that the derivative
of a map 
at 
is
written as 
and consists of an 
matrix called the matrix of partial derivatives of f at :
The derivative of f at represents the best linear
approximation
to f near to .
As an example of calculating a derivative, consider the function from 
to that transforms polar coordinates into Cartesian
coordinates:
The derivative of this particular transformation is
