Question

what's the 1st and 2nd derivative for
y= (1+2x^2)/(1+x^2) what's the 1st and 2nd derivative for
y= (1+2x^2)/(1+x^2) @Mathematics

Answer 1

i got 2x/(1+x^2)^2 for the first one, but i know it has to be wrong bc my graph isn't turning out right

Answer 2

bc?

Answer 3

\[\frac{dy}{dx}\frac{1+2x^2}{1+x^2}=\frac{2x}{(x^2+1)^2}\]
use quotient rule for y'
\[\frac{dy}{dx}\frac{2x}{(x^2+1)^2}=\frac{2-6x^2}{(x^2+1)^3}\]
for y" use product rule and then chain rule what's left.

Answer 4

give me a medal

Answer 5

post areply and i give you

Answer 6

Cindee, did you input it as 2x/(1+x^2)^2

Answer 7

If you input it linearly, you have to include the parentheses

Answer 8

yes i did, it had to sketch the graph by hand. I compared it with the calculator after and it didn't match up. I think i messed up on the algebra when doing to second derivative. Is there any easier or faster why i getting the second derivative without using the quotient rule?

Answer 9

Well, if there's a sqrt in the denominator you can use conjugation to get rid of the sqrt in the denominator, but that's about it. You really can't avoid using quotient rule

Answer 10

sigh* ok it just gets so messy sometimes. Thank you!!

Answer 11

I didn't use the quotient rule on the 2nd derivative.

Answer 12

Do yourself a favor and get a TI-Nspire CAS

Answer 13

we aren't allowed to use calculators for exams..

Answer 14

A shame

Answer 15

like I said in my post:
"for y" use product rule and then chain rule what's left"

I prefer TI89 or TI92 over the Nspire series, for no real reason... lol

Answer 16

@agreene how did you move the denominator to the numerator?

Answer 17

I didnt

Answer 18

TI-Nspire is excellent if you know how to use it

Answer 19

I know why you prefer the old OS types

Answer 20

Quicker input

Answer 21

'Cause I'm poor mostly, lol

Answer 22

Well, the 1st Generation TI-Nspires are only about $50 bucks now

Answer 23

i'm confused then how did you use the product rule to get the second derivative

Answer 24

factor out the 2 and get:
2(d/dx [ x/((x^2+1)^2)]
product rule is:
d/dx (u*v) = v du/dx + u dv/dx
take u = x and v= 1/((x^2+1)^2)
then you are at:
\[2(x(\frac{d}{dx}(\frac{1}{(x^2+1)^2}))+\frac{\frac{d}{dx}(x)}{(x^2+1)^2}\]

Answer 25

Then you can chain rule and start reducing.