hi there, i am actually studying about functional equation.

I got stucked with some derivatives problem,

and where i could find nowhere to refer or study from,

because it seems it is out of university book level.

my question is this :

what does it means by taking derivative with respect to partial derivative?

can anyone visualize this idea to me?

because i couldn't figure out the term with respect to partial derivative,

when it comes to a functional equation,

of which is a differential equations.

For e.g : F(x,y(x),y'(x),y''(x)) , find

of

F(x,y(x),y'(x),y''(x)) /

y' .

How can we write the full solution with partial derivative respect to y' ? and how bout y''?