## goku3 3 years ago can someone help me find the derivative to this equation 2xsqrtx^2+1

1. goku3

$2x \sqrt{x^2+1}$

2. goku3

actually i got all to the end of the i just can figure out how to simlify the damn thing to match the books answer

3. dpaInc

lemme do that again ... i just realized i didn't take the square root..

4. dpaInc

|dw:1333008783149:dw|

5. goku3

4x^2/2sqrtx^2+1 +x^2+1 and i dont know how to simplify this to get 2(2x^2+1)/sqrtx^2+1

6. dpaInc

|dw:1333008899711:dw|

7. dpaInc

factor out the common factor of 2(x^2+1)^(-1/2)

8. dpaInc

|dw:1333009455298:dw|

9. goku3

sorry i dont know what you did this is where am at 2[x(2x)/2sqrtx^2+1+sqrt x^2+1

10. CoCoTsoi

Plz see the attachment

11. CoCoTsoi

Is the photo clear? If not, I can upload another one

12. dpaInc

i can't make out what you wrote for your derivative (@ goku3)

13. goku3

14. CoCoTsoi

15. brinethery

I agree with @CoCoTsoi 's answer.

16. brinethery

It is beauteeeful.

17. goku3

i get lost between step to and three

18. brinethery

Chain rule

19. goku3

why is there two 2x on top

20. brinethery

And product rule... http://tutorial.math.lamar.edu/Classes/CalcI/ProductQuotientRule.aspx

21. CoCoTsoi

one 2x is the original one. another is by diff the equation inside the sqrt

22. brinethery

So say if you have f*g. If you use the product rule, then you'll do: f'*g + f*g'.

23. brinethery

sorry if you couldn't see the tick mark next to the f.

24. goku3

its cool how you get rid of the sqrt on top

25. brinethery

Okay so going from the 3rd to the 4th line: There's 2sqrt(x^2+1) He want's to get it so it has the same denominator as the other term. The den of the other term is sqrt(x^2+1). So with the left term, you have to multiply the numerator and denominator by sqrt(x^2+1). Then you end up with (2sqrt(x^2+1)*sqrt(x^2+1))/sqrt(x^2+1) = (2(x^2+1))/sqrt(x^2+1)

26. brinethery

lol... wants not want's. I type too fast.

27. CoCoTsoi

multiply numerator and denominator with sqrt(x^2+1)

28. goku3

thank you guys so much every time i tried to do it i forgot to add one of the 2x and messed my entire thing up

29. brinethery

We all tend to get lost in the little steps, believe me I've been there. Coco did a great job writing that out.

30. CoCoTsoi

Coz I was lazy for typing it on keyboard so I chose to write it on paper :D

31. goku3

paper is way faster and thank u guys for being so patient with me

32. brinethery

So goku, remember with this problem, you have to use the product rule and then the chain rule since you have stuff inside of that square root.

33. CoCoTsoi

Thanks for giving a chance for us to learn

34. goku3

yeah i will i just have to take my on these problems and not rush them

35. brinethery

Check out paul's online notes if you haven't already, they are great :-)

36. goku3

i have them bookmarked actually