Editing Exact differential (section)

===Definition===
Even if we work in three dimensions here, the definitions of exact differentials for other dimensions are structurally similar to the three dimensional definition. In three dimensions, a form of the type
<math display="block">
 A(x, y, z) \,dx + B(x, y, z) \,dy + C(x, y, z) \,dz
</math>
is called a [[differential form]]. This form is called ''exact'' on an open domain <math>D \subset \mathbb{R}^3</math> in space if there exists some [[Differentiable function|differentiable]] [[scalar function]] <math>Q = Q(x, y, z)</math> defined on <math>D</math> such that
<math display="block">
 dQ \equiv \left(\frac{\partial Q}{\partial x}\right)_{y,z} \, dx
         + \left(\frac{\partial Q}{\partial y}\right)_{x,z} \, dy
         + \left(\frac{\partial Q}{\partial z}\right)_{x,y} \, dz,
 \quad dQ = A \, dx + B \, dy + C \, dz
</math>
throughout <math>D</math>, where <math>x, y, z</math> are [[orthogonal coordinates]] (e.g., [[Cartesian coordinate system|Cartesian]], [[cylindrical]], or [[Spherical coordinate system|spherical coordinates]]). In other words, in some open domain of a space, a differential form is an ''exact differential'' if it is equal to the general differential of a differentiable function in an orthogonal coordinate system.

The subscripts outside the parenthesis in the above mathematical expression indicate which variables are being held constant during differentiation. Due to the definition of the [[partial derivative]], these subscripts are not required, but they are explicitly shown here as reminders.