# Calculus/differentiation (1 Viewer)

#### wandering17

##### Member
Hii's

can someone pls help me using the quotient rule, differentiate

-2x/(x^2+1)

this, and show working out pls?? i feel like im missing a step or something everytime i do it

thanks! much appreciated

#### Rhinoz8142

##### Well-Known Member
Hii's

can someone pls help me using the quotient rule, differentiate

-2x/(x^2+1)

this, and show working out pls?? i feel like im missing a step or something everytime i do it

thanks! much appreciated
this sis the quotient rule formulae..

(u.v')-(u".v)/ v^2

while

u/v

and there u go..

#### HeroicPandas

##### Heroic!
To do quotient rule the most efficiently is to not memorize the formula (well it is the same thing but you don't need to memorize letters)

Here's how I do it..

Step 1: Differentiate top times bottom, MINUS, differentiate bottom times top

$\bg_white (-2)(x^2+1) - (2x)(-2x)$

Step 2: Draw the fraction bar under step 1

$\bg_white \frac{(-2)(x^2+1) - (2x)(-2x)}{???}$

Step 3: Under the fraction bar, write the bottom all squared

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

Hope you understand

Last edited:

##### New Member
-2x/(x^2+1)

Let u=-2x

u'=-2

v=(x^2+1)

v'=2x

Formula= y'=(vu'-uv')/v^2

Hence y'=[(x^2+1)*(-2)-(-2x)(2x)]/(x^2+1)^2

y'=-2x^2-2+4x^2/(x^2+1)^2

y'=2(x^2-1)/(x^2+1)^2

#### dan964

##### what
The other method is to avoid quotient rule and to write it as
$\bg_white -2x*(x^2+1)^{-1}$

and then do the product rule which is easier to remember.

#### braintic

##### Well-Known Member
Use derivative calculator, it will show all necessary steps.
The solution it gave for this question was ridiculously complicated. It would confuse more people than it would help.