Question

Find the derivative of the following function.

Answer 1

\[\frac{ x^2+x-1 }{ x^2-1 }\]

Answer 2

@precal

Answer 3

\[\large \frac{ x^2+x-1 }{ x^2-1 }= \frac{(x^2-1)+x}{x^2-1}\]\[\large =\frac{x^2-1}{x^2-1}+\frac{x}{x^2-1}\]\[\large =1+\frac{x}{x^2-1}\]
Hmm if you split this into a couple fractions like this, it might make things a bit easier :) Now you have quotient rule, but it's not as tricky from here.

Answer 4

Understand how to apply the quotient rule? :D

Answer 5

all i did was use the quotient rule as is. derivative of x^2+x-1 is 2x+1 times x^2-1...

Answer 6

so it would look like this.\[\frac{ 2x(x^2-1)+x^2+x-1+2x^3+2x^2-2x }{ (x^2-1)^2 }\] after the quotient rule and some distributing...

Answer 7

\[\large \frac{ (x^2+x-1)'(x^2-1)-(x^2+x-1)(x^2-1)' }{ (x^2-1)^2 }\]
\[\large =\frac{ (2x+1)(x^2-1)-(x^2+x-1)(2x) }{ (x^2-1)^2 }\]
Oh i see, you did some distributing :) oh man this one is messy :O

Answer 8

I'm not sure what you need help with then, it looks like you're on the right track! :D

Answer 9

Before you distributed, did your setup look like mine? :o that might be a way to check your work at least :D
Because I think i see a bad x in your top, but I could be wrong...

Answer 10

oh shoot it's minus not plus. i keep getting mixed up. I'm gonna try again and i'll reply if i get it right. Thanks!

Answer 11

i got it! thanks!

Answer 12

Yay team \c:/