y = (x^{3}√(x^{2 }+ 1))/(x - 1)

What I did:

I used natural log on both sides.

I brought the exponents into the coefficient.

I also brought the (x - 1) up by doing it to the negative one exponent

Then I used the log properties.

So tell me if this is the correct way:

ln y = 3lnx + (1/2)ln(x^{2 }+ 1) - ln(x - 1)

Then I find the derivative

1/y(dy/dx) = 3/x + (1/2)(1/(x^{2 }+ 1)) - (1/(x - 1))

After that I multiplied both sides by y, then plugged in y, which is the original equation.

So would this be right?

Thanks