# Total differential

From Glossary of Meteorology

## total differential

The total differential of a function whether or not

*f*=*f*(*x*_{1},*x*_{2}, · · ·,*x*_{n}) of*n*variables is defined by the equation*x*_{1},*x*_{2}, · · ·, and*x*_{n}are independent of each other. , , · · ·, and denote the partial derivatives of*f*with respect to*x*_{1},*x*_{2}, · · ·, and*x*_{n}respectively. The total differential*df*represents the change in*f*associated with simultaneous infinitesimal changes in*x*_{1},*x*_{2}, · · ·, and*x*_{n}given by*dx*_{1},*dx*_{2}, · · ·,*dx*_{n}, respectively, to the order of*dx*_{1},*dx*_{2}, · · ·,*dx*_{n}.