Calculus of variation. Minimum surface

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knockout_artist

so df/dy' is yy'/ √(1+y'^2)

then we are supposed to do
y' . [ yy'/ √(1+y'^2) ] - y√(1+y'^2)

how does this bring equation 2 in the image ?

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knockout_artist

imaged rotated :)

formodular

Multiply ##f = y \sqrt{1+y'^2}## by ##1 = \frac{\sqrt{1+y'^2}}{\sqrt{1+y'^2}}## then subtract from ##y' f_y'##.

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