Consider

**z=f(x,y)**If we differentiate

*w.r.t.*

**z***considering*

**x***as constant , we get the partial derivatives as*

**y**

**df/dx***or*

**= dz/dx**

**fx**Similarly keeping

*constant we can differentiate*

**x***w.r.t.*

**z***we get ;*

**y**

**df/dy***or*

**=dz/dy**

**fy**If we differentiate

*again w.r.t.*

**df/dx***keeping*

**x***as constant*

**y**we get the second order partial derivatives

**(d/dx)(df/dx)**If we differentiate

*w.r.t.*

**df/dx**

*, keeping*

**y***as constant ,*

**x**we get another second order partial derivatives

**(d/dy)(df/dx)**Similarly two more derivatives

**(d/dx)(df/dy)**and

**(d/dy)(df/dy) .**