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

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

anonymous · Answer

I'll post what I have so far

anonymous · Answer

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

anonymous · Answer

nvm, I see what you mean

anonymous · Answer

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

anonymous · Answer

$$\frac{- (4+x)}{ (1+x)}$$

anonymous · Answer

Now just use the quotient rule from here

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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.

anonymous · Answer

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

anonymous · Answer

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