Exact differential

In <a href="/facts/Multivariate_calculus/PEs5SgUF">multivariate calculus</a>, a <a href="/facts/Differential_(infinitesimal)/3dxU2Wy2">differential</a> or <a href="/facts/Differential_form/T9gyHtMv">differential form</a> is said to be exact or perfect (exact differential), as contrasted with an <a href="/facts/Inexact_differential/bBGjo3N3">inexact differential</a>, if it is equal to the general differential 
 
 
 
 d
 Q
 
 
 {\displaystyle dQ}
 
 for some <a href="/facts/Differentiable_function/jQqTgLk1">differentiable function</a> 
 
 
 
 Q
 
 
 {\displaystyle Q}
 
 in an <a href="/facts/Orthogonal_coordinates/LLoa2lAJ">orthogonal coordinate system</a> (hence 
 
 
 
 Q
 
 
 {\displaystyle Q}
 
 is a multivariable function <a href="/facts/Dependent_and_independent_variables/dINfzIF2">whose variables are independent</a>, as they are always expected to be when treated in <a href="/facts/Multivariable_calculus/PEs5SgUF">multivariable calculus</a>).
An exact differential is sometimes also called a total differential, or a full differential, or, in the study of <a href="/facts/Differential_geometry/c04XmyLu">differential geometry</a>, it is termed an <a href="/facts/Exact_form/uvEUbzUK">exact form</a>.
The integral of an exact differential over any integral path is <a href="/facts/Conservative_vector_field/MoS3V9aV">path-independent</a>, and this fact is used to identify <a href="/facts/State_function/JThJasbq">state functions</a> in <a href="/facts/Thermodynamics/q4hIx3yP">thermodynamics</a>.

Exact differential open-in-new

Exact differential