Consider a domain
in the *xyz*-space. Suppose now that there exists an invertible function
*g*=(*g*_{1},*g*_{2},*g*_{3}), defined over a domain
in the *uvw*-plane such that
(*x*,*y*,*z*)=( *g*_{1}(*u*,*v*,*w*), *g*_{2}(*u*,*v*,*w*), *g*_{3}(*u*,*v*,*w*)). Moreover suppose that *g* is differentiable over
(i.e. each *g*_{i} is differentiable over
).
Thus, we have:
*f*(*x*,*y*,*z*)=*f*(*g*_{1}(*u*,*v*,*w*), *g*_{2}(*u*,*v*,*w*),*g*_{3}(*u*,*v*,*w*) ).

is called the