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amorfide

Differentiate step by step I don't remember how to do it (4lnx-3)/(4lnx+3)

  • one year ago
  • one year ago

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  1. amorfide
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    would i do (vdu-udv)/v²

    • one year ago
  2. amorfide
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    @cwrw238

    • one year ago
  3. amorfide
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    @Hero can you help?

    • one year ago
  4. zepdrix
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    Are you allowed to simplify your answer before you differentiate? :) Because it's currently written as a pair of conjugates, if we multiply them together it'll simplify very nicely.

    • one year ago
  5. amorfide
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    no do it straight off use substitute v and u if needed

    • one year ago
  6. amorfide
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    actually i do not think method matters xD

    • one year ago
  7. zepdrix
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    Ok :) In that case, it looks like we have the product of two functions involving x. So we'll need to apply the product rule. The one that you posted above is the quotient rule :O we don't want to you that formula. \[\huge (uv)'=u'v+uv'\] This is the one we want :)

    • one year ago
  8. amorfide
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    i am sure it is quotient,...

    • one year ago
  9. zepdrix
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    Oh i didn't see the division symbol in there sorry, it was hidden for some reason lolol

    • one year ago
  10. amorfide
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    i have the answer no method answer is 24/x(4lnx+3)²

    • one year ago
  11. zepdrix
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    I hate that tiny text :)

    • one year ago
  12. zepdrix
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    k you have the right formula then, just need help setting it up? :o

    • one year ago
  13. amorfide
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    well i know which is v and u i dont know the differential of 4lnx -3

    • one year ago
  14. zepdrix
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    Recall this:\[(\ln x)'=\frac{ 1 }{ x }\] So let's apply that to our u. \[\large u=4\ln x - 3\]\[\large u'=4\frac{ 1 }{ x } - 0\] The 4 is just a constant, so we can ignore that while we differentiate.

    • one year ago
  15. amorfide
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    I feel dumb, thank you <3

    • one year ago
  16. zepdrix
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    heh :3

    • one year ago
  17. amorfide
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    well.. i get |dw:1352060900067:dw|

    • one year ago
  18. amorfide
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    if i multiply by x/x will that give me the right answer?

    • one year ago
  19. amorfide
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    @zepdrix

    • one year ago
  20. amorfide
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    so how would i find the gradient of (4lnx-3)/(4lnx+3)

    • one year ago
  21. zepdrix
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    |dw:1352061081956:dw| Hmmm I'm confused how you get 24/x on the top :O

    • one year ago
  22. zepdrix
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    Nevermind I see it now XD

    • one year ago
  23. zepdrix
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    Me so slow today :3

    • one year ago
  24. amorfide
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    i moved on, i need the gradient lol... how?

    • one year ago
  25. zepdrix
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    the gradient? :( mmm I'm in the US, is that what we call the slope i guess? :O

    • one year ago
  26. amorfide
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    yeah slope

    • one year ago
  27. zepdrix
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    Are you trying to form an equation for a particular line tangent to the function? :O We need a specific point along the function to start with if that's the case.

    • one year ago
  28. amorfide
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    crosses the x axis y=(4lnx-3)/(4lnx+3) get the exact value of the gradient

    • one year ago
  29. zepdrix
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    |dw:1352061602252:dw| Understand how we got that particular x value? It's a little bit tricky near the end there.

    • one year ago
  30. amorfide
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    ahh thank you! forget to make it equal to zero my bad xD

    • one year ago
  31. zepdrix
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    Understand how to find the value of the gradient from there? :) Plugging that point into the derivative function and such? :D

    • one year ago
  32. amorfide
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    36e^3/4 ?

    • one year ago
  33. amorfide
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    ahh that is just the denominator my bad (2/3)e^(3/4)

    • one year ago
  34. amorfide
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    that should be -3/4

    • one year ago
  35. zepdrix
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    |dw:1352062210018:dw| Hmm yah that looks right, good job! :)

    • one year ago
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