Question

I cant figure out how to derive this:
f(x)= cos((1+x^2)/(1-x^2))

And then putting in f(sqrt(2))

Thank you!

Answer 1

add the number

Answer 2

what i meant was f ' (sqrt(2))

Answer 3

but i have trouble deriving this

Answer 4

use chain rule

Answer 5

\(\large f(x) = \cos\left(\dfrac{1+x^2}{1-x^2}\right)\)


\(\large f'(x) = -\sin\left(\dfrac{1+x^2}{1-x^2}\right) \times \left(\dfrac{1+x^2}{1-x^2}\right) '\)

Answer 6

^differentiate the inside funciton again - use quotient/product rule

Answer 7

ooh ofcourse!
thank you

Answer 8

Once you're done, do verify ur answer against wolfram's :
http://www.wolframalpha.com/input/?i=%5Ccos%5Cleft%28%5Cdfrac%7B1%2Bx%5E2%7D%7B1-x%5E2%7D%5Cright%29%27

Answer 9

u wlc :)

Answer 10

thank you soo much! i totally get it now!

Answer 11

np :) good to hear :D