Найдите производную второго порядка y=x/(x-3),

Y = x/(x-3)

y'= [ x'(x-3)-x*(x-3)'] / (x-3)² = ( x-3-x)/(x-3)² = -3/(x-3)² = -3 * 1/(x-3)²

y''= -3 [ 1'*(x-3)² - 1* [(x-3)² ]'   ] / (x-3)⁴  = -3* [ x²-6x+9-2(x-3) ] /(x-3)⁴ = 

= -3* [ x²-6x+9-2x+6 ] /(x-3)⁴ = -3*( x²-8x+15+1-1)/(x-3)⁴= -3*[ (x-4)²-1 ] / (x-3)⁴=
=-3*[ (x-4-1)(x-4+1) ] /(x-3)⁴ = -3* [ (x-5)(x-3) ] / (x-3)⁴= -3*(x-5) / (x-3)³