This could also be written as

`del/(delx)[(delF)/(dely)]`

This expression means

Find the partial derivative with respect to x of the partial derivative with respect to y.

In our example above, F(x,y) = y + 6 sin x + 5y2, we found

`(delF)/(dely)=1+10y`

To find `(del^2F)/(delxdely)`, we need to find the partial derivative with respect to x of `(delF)/(dely)`.

`(del^2F)/(delxdely)=del/(delx)[(delF)/(dely)]`

`=del/(delx)[1+10y]`

`=0`

Since y is a constant (when we are considering differentiation with respect to x), its derivative is just 0.