## anonymous 4 years ago can someone help me find the derivative to this equation 2xsqrtx^2+1

1. anonymous

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

2. anonymous

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. anonymous

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

4. anonymous

|dw:1333008783149:dw|

5. anonymous

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. anonymous

|dw:1333008899711:dw|

7. anonymous

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

8. anonymous

|dw:1333009455298:dw|

9. anonymous

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

10. anonymous

Plz see the attachment

11. anonymous

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

12. anonymous

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

13. anonymous

14. anonymous

15. anonymous

I agree with @CoCoTsoi 's answer.

16. anonymous

It is beauteeeful.

17. anonymous

i get lost between step to and three

18. anonymous

Chain rule

19. anonymous

why is there two 2x on top

20. anonymous

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

21. anonymous

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

22. anonymous

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

23. anonymous

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

24. anonymous

its cool how you get rid of the sqrt on top

25. anonymous

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. anonymous

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

27. anonymous

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

28. anonymous

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. anonymous

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. anonymous

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

31. anonymous

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

32. anonymous

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. anonymous

Thanks for giving a chance for us to learn

34. anonymous

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

35. anonymous

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

36. anonymous

i have them bookmarked actually