Calculus of Variations Derivation of Euler Lagrange 1

Get the full course here
Support me on Patreon here

[isobar]

So confusing for me, at 3.38 you use ordinary differentiation then go onto partial differentiation, Why, if we are only the plane [single variable calculus]. Also at 8.17 you use partial f wrt x multiplied by delta y...shouldn't the partial f wrt x be multiplied by delta x to give the change in y [the change in height] ? Really would appreciate some clarification, thanks Ross.