# Math Help - Logarithmic Differentiation...8x or 8

1. ## Logarithmic Differentiation...8x or 8

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.

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

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.

2. ## Re: Logarithmic Differentiation...8x or 8

i think there is a printing mistake in the text book if the answer in the text is correct then -15x + 8x can be added to -7x

3. ## Re: Logarithmic Differentiation...8x or 8

The correct answer is ((3x^2-15x+8)x)/(2x(x-1)^3 sqrt(3x-2)) . do it once again and correctly substitute the value of y

4. ## Re: Logarithmic Differentiation...8x or 8

i think u had done mistake in substituting the value of y there is x^2 in y so one x gets cancelled while substituting and other remains there.

5. ## Re: Logarithmic Differentiation...8x or 8

Originally Posted by binu01234
The correct answer is ((3x^2-15x+8)x)/(2x(x-1)^3 sqrt(3x-2)) . do it once again and correctly substitute the value of y
Yes, but notice the x on top and 2x in the bottom. This is reduced to my original answer which is:

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

It feels good to know that I got the right answer alone. I am not taking calculus 1 in a formal, college class arena. I am learning on my own. Not too bad for someone who is not a math major. Thanks again for your input.

6. ## Re: Logarithmic Differentiation...8x or 8

Originally Posted by binu01234
i think u had done mistake in substituting the value of y there is x^2 in y so one x gets cancelled while substituting and other remains there.
No error at my end. It is a simple typo, which is typical in most math textbooks.

7. ## Re: Logarithmic Differentiation...8x or 8

Correction:

The answer is solved for y prime not y double prime. This was my typo.