## anonymous 3 years ago Easiest way to go about taking this derivative? Power rule, chain rule and quotient rule is kind of ugly.

1. anonymous

$f(x) =\sqrt{\frac{ x-1}{ x+1}}$

2. anonymous

chain rule first then quotient rule

3. anonymous

and it isnt ugly at all. The higher u go, the more 'uglier' it gets. dont be afraid of 'ugly' solutions

4. anonymous

oops supposed to be 1-x and 1+x

5. anonymous

still doesnt matter just flip the sings

6. anonymous

|dw:1353220538034:dw|

7. anonymous

chain rule the exponent 1/2 then differentiate the one inside the bracket using quotient rule

8. anonymous

|dw:1353220581666:dw|

9. anonymous

yup

10. anonymous

that's ugly.

11. anonymous

it really isnt ugly at all... i have seen even uglier ones at my level

12. anonymous

just make the exponent -1/2 into a square root and put it beside the (1+x) ^2

13. anonymous

same with the 2 in the denominator

14. anonymous

This is for a first derivative analysis... It is ugly to find zeroes.

15. anonymous

|dw:1353220820451:dw|

16. anonymous

|dw:1353220855332:dw|

17. anonymous

what are you trying to find?

18. anonymous

first and second derivative analysis

19. anonymous

for turning points and maximum/minimum?

20. anonymous

max, min, inflections

21. anonymous

no solution then

22. anonymous

there is a min at x=1