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
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.
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.