We are trying to determine the derivative of
y=(x^2)/(x-1)
I use the Quotient Rule to figure this out and always come up with y’=0"
y’=(f’g-g’f)/g^2
= ((2x)(x-1) - (1)(x^2))/x^2-2x+1
= 2x^2-2x-x^2/x^2-2x+1
= x^2-2x/x^2-2x+1
= 1 * 0/1
Okay, I know I’m making an arithmetic error. What is it? Can I not cancel out x^2-2x?
You’ve got x(x-2)/(x-1)(x-1).
None of that cancels out.
For reference, my TI-89 graphing calculator says the answer is:
y’ = x(x-2) / (x-1)^2
With the caveat that I haven’t done derivatives by hand for a while now, I quite simply cannot figure out what the heck you’re doing with that 1*0/1 step. Where are you getting that from? Just factor out the step above that and it looks like you’ll get the answer my calc gives.
It doesn’t cancel like that. What’s 4/(4 + 1) equal to? This is a pretty simple problem. I think if you just take a good, long look at it you’ll see what’s up.