Hello guys
I have this function https://www.wolframalpha.com/input/?i=arcsin((2x)/(x^2+2)):
. . . . .\(\displaystyle f(x)\, =\, \arcsin\left(\dfrac{2x}{x^2\, +\, 2}\right)\)
I did the first and the second derivative of this function, but I dont know how to edit it to calculate inflection point correctly.
Can somebody help me?
Second derivation
http://forum.matematika.cz/upload3/img/2016-11/22743_mathtex.gif
. . . . .\(\displaystyle \left(\dfrac{-2x^2\, +\, 4}{\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\,(x^2\, +\, 2)}\right)'\)
. . . . . . . .\(\displaystyle =\, \dfrac{-4x\, \left(\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right)\, -\, 2\, (2\, -\, x^2)\, \left(\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right)'}{\left[\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right]^2}\)
. . . . . . . .\(\displaystyle =\, \dfrac{-4x\, \left(\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right)\, -\, (4\, -\, 2x^2)\, \left(2x\, \sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, +\, (x^2\, +\, 2)\, \frac{1}{2}\, \left((x^2\, +\, 2)^2\, -\, 4x^2)^{-1/2}\, \left(2\, (x^2\, +\, 2)\, 2x\, -\, 8x\right)\right)\right)}{\left[\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right]^2}\)
I tried to edit it like this
https://postimg.org/image/v99sd4csr/
I will be glad for any help.
Thanks
I have this function https://www.wolframalpha.com/input/?i=arcsin((2x)/(x^2+2)):
. . . . .\(\displaystyle f(x)\, =\, \arcsin\left(\dfrac{2x}{x^2\, +\, 2}\right)\)
I did the first and the second derivative of this function, but I dont know how to edit it to calculate inflection point correctly.
Can somebody help me?
Second derivation
http://forum.matematika.cz/upload3/img/2016-11/22743_mathtex.gif
. . . . .\(\displaystyle \left(\dfrac{-2x^2\, +\, 4}{\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\,(x^2\, +\, 2)}\right)'\)
. . . . . . . .\(\displaystyle =\, \dfrac{-4x\, \left(\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right)\, -\, 2\, (2\, -\, x^2)\, \left(\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right)'}{\left[\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right]^2}\)
. . . . . . . .\(\displaystyle =\, \dfrac{-4x\, \left(\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right)\, -\, (4\, -\, 2x^2)\, \left(2x\, \sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, +\, (x^2\, +\, 2)\, \frac{1}{2}\, \left((x^2\, +\, 2)^2\, -\, 4x^2)^{-1/2}\, \left(2\, (x^2\, +\, 2)\, 2x\, -\, 8x\right)\right)\right)}{\left[\sqrt{\strut (x^2\, +\, 2)^2\, -\, 4x^2\,}\, (x^2\, +\, 2)\right]^2}\)
I tried to edit it like this
https://postimg.org/image/v99sd4csr/
I will be glad for any help.
Thanks
Last edited by a moderator:
