I found this interesting question in my textbook. I am to solve this rational function via implicit differentiation. This question is from a section of the chapter titled LOGARITHMIC DIFFERENTIATION.

Find y double prime.

y = [x^2 * sqrt{3x-2}]/(x-1)^2

After much work, I found y" to be the following monster:

[(2/x)+3/(2(3x-2)-2/(x-1)]*y where y is the original rational function given.

My Answer is:

y" = (3x^2-15x+8)/2(x-1)^3*sqrt{3x-2}

The book's answer is:

y" = (3x^2-15x+8x)/2(x-1)^3*sqrt{3x-2}

My question: Where did 8x come from in the numerator? Can this be a typo?

I worked out the problem several times and my answer has not included 8x in the numerator.