Question

differentiate y = (x-1) (x-2)/√x​

Answer 1

Answer:

y=(x-1)(x-2)/x^1/2. = (x^2-3x+2)/x^1/2

dy/dx=[√x.(2x-3)-1/2√x.(x^2-3x+2)]/(√x)^2

dy/dx =[2x(2x-3)-(x^2-3x+2)]/2x√x.x

dy/dx =[4x^2–6x-x^2+3x-2]/2x√x.

dy/dx=(3x^2–3x-2)/2.x.√x. Answer.

Second-Method :-

Braking log of both the sides.

log y = log(x-1)+log(x-2) -1/2.log x

1/y.dy/dx = 1/(x-1) +1/(x-2) - 1/2x.

dy/dx= y.[2x(x-2)+2x(x-1)-(x-1)(x-2)]/2x.(x-1).(x-2).

dy/dx = {(x-1).(x-2)/√x}.[2x^2–4x+2x^2–2x-x^2+3x-2]/2x.(x-1).(x-2).

dy/dx =(3x^2–3x-2)/2x√x. Answer.