# How can I do partial derivation for F(y,y') with respect to y'? [closed]

This is a part of a question on the master/doctor degree graduate school entrance test for Tokyo Univ. in 2016.

The conditions are below

( )

Here is the question.

I have to make a differential equation using y, y', and c.

However, I don't have any ideas to partially derivate F with respect to y'.

I can't ignore y in F(y,y') because it has a relationship with y, can I?

Please tell me how to deal with this problem.

D[y Sqrt[1 + y' ^2], y']

• No, if you say dF[y,y']/dy' you mean: You treat y and y' as the only variables, independent of what y means. – Daniel Huber Mar 11 at 8:38