y(x) = 8.x^6/(x-1), then.d^4y/dx^4 = ?
show workings!plz
y = 8x^2/(x-1)
y' = ( (x-1)(16x) - 8x^2) )/(x-1)^2
= (16x^2 - 16x - 8x^2)/(x-1)^2
= (8x^2 - 16x)/(x-1)^2
y'' = ( (x-1)^2 (16x - 16) - (8x^2 - 16x)(2)(x-1) )/(x-1)^4
= (16x - 16)/(x-1)^4
= 16(x-1)/(x-1)^4 = 16/(x-1)^3
Well, that went well, from here on it is easy
y'' = 16(x-1)^-3
y''' = -48(x-1)^-4
y '''' = 192(x-1)^-5 or 192/(x-1)^5