1) формула: (U/V)" = (U'V - UV")/V²
f'(x) = (9*√(x² +1) - 9x * 1/2√х * 2х ) /(х² +1) = (9(х² +1) -9х²)/(х² +1)√(х² + 1).
f'(2√2) = (9*10 - 9*8)/10√9 = 8/30 = 4/15
2) формула: (U/V)" = (U'V - UV")/V²
f'(x) = (2*√(x²+1) - (2x +1) * 1/2√(x² +1) * 2x) /(x² +1)=
= (2x² +2 -2x² - x)/(x² +1)*√(x² +1) = (2 - x)/(x² +1)√(√x² +1).
f'(√3) = (2 - √3)/(10*√10)
3) формула: (U*V)" = U'V + UV"
f'(x) = 2x√(x² -1) + (x² -1) * 1/2√(х² - 1) * 2х= (2х(х² -1) +х(х² -1))/√(х² -1) =
= (2х³ -2х +х³ -х)/√(х² -1) =( 3х³ -3х)/√(х² -1)
f'(√2) = (3√8 - 3√2) /√3 = 3√2/√3 = √6