## anonymous 3 years ago just wondering how to proceed with this problem.

1. anonymous

Use the appropriate rule or combination of rules to find the derivative of the function defined below. y=$(16x-4)\sqrt{8x-2}$

2. anonymous

i know i have to use my product rule, when i do that i get: (16x-4)(1/2)(8x-2)^-1/2 + (8x-2)^1/2 *16

3. hartnn

u forgot chain rule for (8x-2)

4. anonymous

oh times 8 in there lol. i had that wrote down, lol just forgot to type it.

5. hartnn

then u are correct

6. anonymous

okay so that i got: $\frac{ 4(16x-4) }{ \sqrt{8x-2} }+16\sqrt{8x-2}$

7. hartnn

absolutely correct!

8. anonymous

would i take my 4 out of the numerator so i got 16(4x-1) ?

9. hartnn

thats not much of a simplification, but u can !

10. anonymous

is tehre a way to further simplify this> my answer isn't matching any of the answers on my assingment (this one is a multiple choice)

11. hartnn

what are the options ? u can factor out 16 from both the terms..

12. anonymous

a) 16- 4/squrt8x-2 B)16(squrt8x-2)+32 times 16x-4/squrt8x-2 c)16-16/squrt8x-2 d)64/squrt8x-2 e)32*2^1/2*x^1/2 -16*2^1/2+(16-4x)/squrt8x-2 f)8*csgn(4x-1)*2^1/2 g)16*squrt8x-2+4(16x-4/squrt8x-2) h)8(16x-4)(squrt8x-2)

13. hartnn

ohh, u can cross-multiply to get the common denominator as $$\sqrt{}8x-2$$

14. anonymous

so then i have$4(16x-4)+16\sqrt{8x-2}(\sqrt{8x-2})$

15. anonymous

??

16. hartnn

which is? $$\sqrt{8x-2}\sqrt{8x-2}=8x-2$$

17. anonymous

i had 320x-16 as my numerator but that's not there as an answer either.

18. anonymous

19. hartnn

checking, wait..your c option is weird...16-16=0

20. anonymous

$16-\frac{ 16 }{ \sqrt{8x-2} }$

21. anonymous

that's what it actually is, it's a little weird when i wrote it the other way lol..

22. anonymous

so is that right tho?

23. anonymous

My answer's the denom. cancel out! However the way your post the option too complicated to read !!!

24. anonymous

25. anonymous

$a) 16-\frac{ 4 }{ \sqrt{8x-2} }$

26. anonymous

= 24 √ ( 8x -1)

27. anonymous

$b) 16\sqrt{8x-2}+32*\frac{ 16x-4 }{ \sqrt{8x-2} }$

28. anonymous

$c)16-\frac{ 16 }{ 8x-2 }$

29. anonymous

$d)\frac{ 64 }{ \sqrt{8x-2} }$

30. anonymous

$e) 32*2^{\frac{ 1 }{ 2 }}*x^\frac{ 1 }{ 2 }-16*2^\frac{ 1 }{ 2 }+(16x-4)*\frac{ 2^\frac{ 1 }{ 2 } }{ x \frac{ 1 }{ 2 } }$

31. anonymous

$f)8*csgn(4x-1)*2^\frac{ 1 }{ 2 }$

32. anonymous

are you sure?

33. anonymous

$g)16\sqrt{8x-2}+4\frac{ 16-4x }{ \sqrt{8x-2}}$

34. anonymous

no idea hah.

35. anonymous

$h)8(16-4x)(\sqrt{8x-2}$

36. hartnn

isn't g) option the same thing what we got ?

37. anonymous

omg.. look at that.

38. anonymous

hhaha so it is!!!

39. anonymous

if you wanna check out my lastest/last question that would be great!

40. anonymous

So it turns out that there's no need to simplified =)

41. anonymous