Question

I can't seem to get the correct answer to this problem. I need to find the derivative of this problem algebraically.

f(x) = 4 - 3x - x^2/x^2 - 1

Answer 1

I'll post what I have so far

Answer 2

\[f \prime(x) = (x ^{2}-1)(-3-2x)-(4-3x-x ^{2})(2x)/(x ^{2}-1)^{2}\]

Answer 3

nvm, I see what you mean

Answer 4

\[\frac{4-3x-x^2}{x^2-1}\]
\[\frac{-(-1+x) (4+x))}{(-1+x) (1+x)}\]

Answer 5

\[\frac{- (4+x)}{ (1+x)}\]

Answer 6

Now just use the quotient rule from here

Answer 7

\[\frac{(- 4-x)'(1+x)-(1+x)'(- 4-x))}{ (1+x)^2}\]

Answer 8

\[\frac{-1(1+x)- 1(-4-x)}{\left(1+x^2\right)}\]
\[\frac{3}{1+x^2}\]

Answer 9

Oh I see, you factored out everything first and then did the derivative of the quotient rule. I tried to do it the other way, and coudln't figure out how to get that final answer. Guess I should keep that in mind then. Thanks.

Answer 10

Yeah, otherwise you would have a error prone mess of a function to differentiate

Answer 11

That's exactly what happened when I did it...lol