## baldymcgee6 2 years ago Easiest way to go about taking this derivative? Power rule, chain rule and quotient rule is kind of ugly.

1. baldymcgee6

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

2. irkiz

chain rule first then quotient rule

3. irkiz

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

4. baldymcgee6

oops supposed to be 1-x and 1+x

5. irkiz

still doesnt matter just flip the sings

6. irkiz

|dw:1353220538034:dw|

7. irkiz

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

8. baldymcgee6

|dw:1353220581666:dw|

9. irkiz

yup

10. baldymcgee6

that's ugly.

11. irkiz

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

12. irkiz

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

13. irkiz

same with the 2 in the denominator

14. baldymcgee6

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

15. irkiz

|dw:1353220820451:dw|

16. baldymcgee6

|dw:1353220855332:dw|

17. irkiz

what are you trying to find?

18. baldymcgee6

first and second derivative analysis

19. irkiz

for turning points and maximum/minimum?

20. baldymcgee6

max, min, inflections

21. irkiz

no solution then

22. baldymcgee6

there is a min at x=1