Derivatives Quotient Rule

**oregon88** · May 17th 2010, 12:47 PM

In the problem f(x) = -1/x^2+1 finding the derivative using the quotient rule.

the solution would be -x^2+2x-1/(x^2+1)^2?

It seems right but im not sure.

**e^(i*pi)** · May 17th 2010, 12:58 PM

Originally Posted by oregon88

In the problem f(x) = -1/x^2+1 finding the derivative using the quotient rule.

the solution would be -x^2+2x-1/(x^2+1)^2?

It seems right but im not sure.

I don't get that answer, perhaps you could post your working?

$f'(x) = \frac{2x}{(x^2+1)^2}$

Wolfram gets the same answer I do. If you are unsure about how to use the quotient rule here the chain rule works equally well

Spoiler:

**oregon88** · May 17th 2010, 01:09 PM

$f(x)=-x/x^2+1$

$f'(x)=(x^2+1)d/dx(-x)-(-x)d/dx(x^2+1)/(x^2+1)^2$

$(x^2+1)(-1)-(-x)(2x)/(x^2+1)^2$

$-x^2+2x-1/(x^2+1)^2$

Is what I came up with

**e^(i*pi)** · May 17th 2010, 01:20 PM

Originally Posted by oregon88

$f(x)=-x/x^2+1$

$f'(x)=(x^2+1)d/dx(-x)-(-x)d/dx(x^2+1)/(x^2+1)^2$

$(x^2+1)(-1)-(-x)(2x)/(x^2+1)^2$

$-x^2+2x-1/(x^2+1)^2$

Is what I came up with

Hold on, you said $f(x) = -\frac{1}{x^2+1}$ in the OP. Which one is correct?

Your differentiating is correct but your simplification on the third line is not - there should be no x term. Plus be more clear with your syntax using brackets

$u = -x \: \rightarrow \: u' = -1$

$v = x^2+1 \: \rightarrow \: v' = 2x$

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

**oregon88** · May 17th 2010, 01:34 PM

The original problem is

$<br /> f(x) = \frac {-x}{x^2+1}<br />$

Sorry about that, I see where I messed up on the third line I did not factor the (-x)(2x) on my paper. Thanks for the help e^(i*pi)

Thread: Derivatives Quotient Rule

LinkBack

Thread Tools

Display

Derivatives Quotient Rule

Similar Math Help Forum Discussions

[SOLVED] Quotient rule for derivatives

Derivatives: Product/Quotient Rule

Product and Quotient Rule with Derivatives

Intro to Derivatives - Quotient Rule

derivatives using the quotient rule

Search Tags