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anonymous

  • 5 years ago

y'' for y= (x^2+9)^4

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  1. anonymous
    • 5 years ago
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    Take the first derivative using the chain rule and then take the derivative of that.

  2. anonymous
    • 5 years ago
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    Second derivative will require both the chain rule and the product rule.

  3. anonymous
    • 5 years ago
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    could you show me it worked step by step

  4. anonymous
    • 5 years ago
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    \[y'=4(x^2+9)^3(2x)\]

  5. anonymous
    • 5 years ago
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    That's the first derivative. Do you see where things might have come from?

  6. anonymous
    • 5 years ago
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    yes i had it all right except the 2x and thats by taking the derivative of the things inside the brackets

  7. anonymous
    • 5 years ago
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    Yes :) that is the chain rule.

  8. anonymous
    • 5 years ago
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    So now we move on to the second derivative which involves the product rule.

  9. anonymous
    • 5 years ago
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    Do you know how to use the product rule?

  10. anonymous
    • 5 years ago
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    okay i got.... 4(x^2+9)^3 (2) + (2x) 12(x^2+9)^2

  11. anonymous
    • 5 years ago
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    Very close. First half is correct. Second half you forgot something.

  12. anonymous
    • 5 years ago
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    what did i forget

  13. anonymous
    • 5 years ago
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    oh do the product rule to finish?

  14. anonymous
    • 5 years ago
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    the books has 8(x^2+9)^3 + 48x^2(x^2+9)^2 = 8(x^2+9)^2(7x^2+9)

  15. anonymous
    • 5 years ago
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    Well the book is correct lol. All you forgot in your was the chain rule on the second half. Should have been (2x)12(x^2+9)(2x) that 2x on the end is what you forgot.

  16. anonymous
    • 5 years ago
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    why is the 2x at the end as well?

  17. anonymous
    • 5 years ago
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    Ok so when you did the second half of the product rule you can say to yourself (2x) times the derivative of the function. Well the derivative of that function 4(x^2+9)^3 is 12(x^2+9)^(2) times the chain rule (2x).

  18. anonymous
    • 5 years ago
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    okay so now where do they get their answer

  19. anonymous
    • 5 years ago
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    got the first part, but didnt get it after the simplifying

  20. anonymous
    • 5 years ago
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    They probably multiplied stuff out and then it eventually got them to that answer. Truthfully, I have never seen a teacher who would not accept the first answer you have. The other answer is just tedious work.

  21. anonymous
    • 5 years ago
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    okay thanks!

  22. anonymous
    • 5 years ago
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    Actually I just looked at their second answer and you could factor...

  23. anonymous
    • 5 years ago
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    okay could you help me with a ln y''?

  24. anonymous
    • 5 years ago
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    Sure.

  25. anonymous
    • 5 years ago
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    okay. I am horrible at ln problems but here is the original y'' for y= ln x/x^2

  26. anonymous
    • 5 years ago
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    Ok this is a quotient rule problem or can be a product rule if you rearrange it. Take your pick.

  27. anonymous
    • 5 years ago
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    SO IT COULD BE (LN X)(-X^2)

  28. anonymous
    • 5 years ago
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    Well could be lnx(x^-2). Normally a lot of people prefer to use the product rule when possible, but it's a little easier.

  29. anonymous
    • 5 years ago
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    OH OKAY

  30. anonymous
    • 5 years ago
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    what is ln x '

  31. anonymous
    • 5 years ago
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    The derivative of lnx is 1/x

  32. anonymous
    • 5 years ago
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    oh yeah sorry

  33. anonymous
    • 5 years ago
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    No worries :)

  34. anonymous
    • 5 years ago
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    okay so y' is lnx(-2x^-3) + (x^-2)(1/x)

  35. anonymous
    • 5 years ago
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    Yes. :)

  36. anonymous
    • 5 years ago
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    okay now im going to need some help..lol

  37. anonymous
    • 5 years ago
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    With simplifying?

  38. anonymous
    • 5 years ago
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    no just straight so i can see what to do

  39. anonymous
    • 5 years ago
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    I'm confused. So what do you need help on? Sorry lol

  40. anonymous
    • 5 years ago
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    second derivative

  41. anonymous
    • 5 years ago
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    Ah. Ok. Well you can use the product rule again for the second derivative, but twice. So use the product rule for the lnx(-2x^-3) and then add that with the result of the product rule of (x^-2)(x^-1). I rewrote 1/x so it's easier to see.

  42. anonymous
    • 5 years ago
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    okay cool

  43. anonymous
    • 5 years ago
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    can you show me it worked out?

  44. anonymous
    • 5 years ago
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    Here is the working

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