B Calculus of variation. Minimum surface

[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 ?

 

[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 $y' f_y'$.