Question

can someone find the first and second derivative of this function?

Answer 1

\[\frac{ x }{ x ^{2}+1 }\]

Answer 2

(d/dx(x) * (x^2+1)- d/dx(x^2+1)*x)/(x^2+1)^2

Answer 3

tell the answer to that

Answer 4

don't u think it can be easy if we use division formula of derivation

Answer 5

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

Answer 6

this is the quotient rule^^^

Answer 7

from division formula:
[x^2+1(d/dy x) - x (d/dy x^2 + 1)]/(x^2 + 1)^2

Answer 8

first derivative is: (1-x^2)/(x^2+1)^2

Answer 9

well i didn't saw that !! :)

Answer 10

Second derivative is (2x)(x^2-3)/(x^2+1)^3

Answer 11

wait, thats what i got for the second derivative

Answer 12

ok. Good. And now you have to graph both derivatives?

Answer 13

I found the critical points, were its concave up and down, increasing and decreasing. Point of point of inflection, mas and min. But I don't know how to draw the graph

Answer 14

Are you talking about the first derivative now?

Answer 15

I have to draw the graph by hand, only using the information I found.

Answer 16

Since you have all the info, I would suggest you look at Wolframalpha.com and try and understand how you could get the graph from the points you found:
https://www.wolframalpha.com/input/?i=y%3D%281-x^2%29%2F%28x^2%2B1%29^2

Answer 17

I would say create a char for all your data

(x, y) | f ' (x) | f ''(x) | Description

^ It helps when understanding how concavity and relative max and mins can be found too.

Answer 18

oh i forgot to mention put f (x) after (x. y) xD

Answer 19

when finding if a function is increasing or decreasing , you would sub the test values into the first derivative right?

Answer 20

wait, i know were I went wrong

Answer 21

a very simple, multiplication error

Answer 22

Yeah. create a number line CP=Critical points.

Answer 23

I just made a multiplication error when doing the number line, its fine now. Thanks everyone

Answer 24

This number line is for the first derivative, it'll tell you where the function is increasing and decreasing by testing points between the critical #'s.These numbers tested will yield a negative or positive value when plugging into the original function, f(x)

Answer 25

Awesome!