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amorfide

  • 2 years ago

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

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  1. amorfide
    • 2 years ago
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    would i do (vdu-udv)/v²

  2. amorfide
    • 2 years ago
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    @cwrw238

  3. amorfide
    • 2 years ago
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    @Hero can you help?

  4. zepdrix
    • 2 years ago
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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.

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

  6. amorfide
    • 2 years ago
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    actually i do not think method matters xD

  7. zepdrix
    • 2 years ago
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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 :)

  8. amorfide
    • 2 years ago
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    i am sure it is quotient,...

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

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

  11. zepdrix
    • 2 years ago
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    I hate that tiny text :)

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

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

  14. zepdrix
    • 2 years ago
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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.

  15. amorfide
    • 2 years ago
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    I feel dumb, thank you <3

  16. zepdrix
    • 2 years ago
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    heh :3

  17. amorfide
    • 2 years ago
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    well.. i get |dw:1352060900067:dw|

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

  19. amorfide
    • 2 years ago
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    @zepdrix

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

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

  22. zepdrix
    • 2 years ago
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    Nevermind I see it now XD

  23. zepdrix
    • 2 years ago
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    Me so slow today :3

  24. amorfide
    • 2 years ago
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    i moved on, i need the gradient lol... how?

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

  26. amorfide
    • 2 years ago
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    yeah slope

  27. zepdrix
    • 2 years ago
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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.

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

  29. zepdrix
    • 2 years ago
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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.

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

  31. zepdrix
    • 2 years ago
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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

  32. amorfide
    • 2 years ago
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    36e^3/4 ?

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

  34. amorfide
    • 2 years ago
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    that should be -3/4

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

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