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iop360 Group Title

Let y = (7/x^3)(√196x^6 +364x^2 + (169/x^2)) Find the derivative of y. Hint: Simplify y before computing the derivative. Answer: (-364/x^5)

  • one year ago
  • one year ago

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  1. iop360 Group Title
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    does anyone know how to simplify the equation first before taking it's derivative?

    • one year ago
  2. ChmE Group Title
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    can you rewrite the equation using the equation tool on this site. It is tough to see in this form.

    • one year ago
  3. iop360 Group Title
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    yep

    • one year ago
  4. iop360 Group Title
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    \[y = \frac{ 7 }{ x^3 }\sqrt{196x^6 + 364x^2 + \frac{ 169 }{ x^2 }}\]

    • one year ago
  5. iop360 Group Title
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    Answer is \[\frac{ dy }{ dx } = \frac{ -364 }{ x^5 }\]

    • one year ago
  6. ChmE Group Title
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    I don't know how to simplify the radical. I would only know how to differentiate right away and it'll get messy

    • one year ago
  7. iop360 Group Title
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    ok thanks anyway

    • one year ago
  8. iop360 Group Title
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    you would use the product rule right?

    • one year ago
  9. ChmE Group Title
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    ya.

    • one year ago
  10. ChmE Group Title
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    I'm doing it too. it's getting pretty rough

    • one year ago
  11. iop360 Group Title
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    \[y' = -21x ^{-4} (196x^6 + 364x^2 + 169x^{-2})^{1/2} + 7x ^{-3}(\frac{ 1 }{ 2 } (196x^6 + 364 + 169x ^{-2})^{-1/2}(1176x^5 +728x -338x ^{-3})^{-1/2}\]

    • one year ago
  12. iop360 Group Title
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    whoops lol

    • one year ago
  13. iop360 Group Title
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    simplifying is the hardest part

    • one year ago
  14. zepdrix Group Title
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    Hmm there is something going on inside this square root, I'm trying to figure it out. Not quite there yet, but I think it's not long off. 196 = 14^2 169=13^2 Hmmmm

    • one year ago
  15. zepdrix Group Title
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    OH! yes found it! :)

    • one year ago
  16. zepdrix Group Title
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    364 = 2 (13*14)

    • one year ago
  17. zepdrix Group Title
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    (14x^4 + 13)^2 I think it'll simplify like that.

    • one year ago
  18. ChmE Group Title
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    nice

    • one year ago
  19. iop360 Group Title
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    so how would this look like

    • one year ago
  20. iop360 Group Title
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    after simplifying?

    • one year ago
  21. zepdrix Group Title
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    |dw:1348968835510:dw| Hmm, I think it simplifies like this, looks much easier to deal with :) I got lazy on the multiplying there hehe

    • one year ago
  22. iop360 Group Title
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    thanks

    • one year ago
  23. ChmE Group Title
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    I got the same thing. great job finding the factorization pattern @zepdrix

    • one year ago
  24. iop360 Group Title
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    how it go from the original to this though

    • one year ago
  25. ChmE Group Title
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    Ok I'll type this one out

    • one year ago
  26. ChmE Group Title
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    I'm going to leave off the radical for now ok?

    • one year ago
  27. iop360 Group Title
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    k

    • one year ago
  28. ChmE Group Title
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    \[196x ^{6}+363x ^{2}+\frac{ 169 }{ x ^{2} }\]Find a common denominator and add\[\frac{ 196x ^{8}+364x ^{4}+169 }{ x ^{2} }\]rewrite the constants\[\frac{ 14*14x ^{8}+2*14*13x ^{4}+13*13 }{ x ^{2} }\]You still with me so far

    • one year ago
  29. ChmE Group Title
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    notice that the numerator looks just like a polynomial

    • one year ago
  30. iop360 Group Title
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    yep

    • one year ago
  31. ChmE Group Title
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    \[\frac{ (14x ^{4}+13)(14x^{4}+13) }{ x ^{2}}\]

    • one year ago
  32. iop360 Group Title
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    oh alright

    • one year ago
  33. ChmE Group Title
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    \[\frac{ \sqrt{(14x^{4}+13)^{2}} }{ \sqrt{x^{2}} }\]

    • one year ago
  34. ChmE Group Title
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    You probably see it now

    • one year ago
  35. iop360 Group Title
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    thanks!

    • one year ago
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