amorfide
  • amorfide
Differentiate step by step I don't remember how to do it (4lnx-3)/(4lnx+3)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
amorfide
  • amorfide
would i do (vdu-udv)/v²
amorfide
  • amorfide
@cwrw238
amorfide
  • amorfide
@Hero can you help?

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zepdrix
  • zepdrix
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.
amorfide
  • amorfide
no do it straight off use substitute v and u if needed
amorfide
  • amorfide
actually i do not think method matters xD
zepdrix
  • zepdrix
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 :)
amorfide
  • amorfide
i am sure it is quotient,...
zepdrix
  • zepdrix
Oh i didn't see the division symbol in there sorry, it was hidden for some reason lolol
amorfide
  • amorfide
i have the answer no method answer is 24/x(4lnx+3)²
zepdrix
  • zepdrix
I hate that tiny text :)
zepdrix
  • zepdrix
k you have the right formula then, just need help setting it up? :o
amorfide
  • amorfide
well i know which is v and u i dont know the differential of 4lnx -3
zepdrix
  • zepdrix
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.
amorfide
  • amorfide
I feel dumb, thank you <3
zepdrix
  • zepdrix
heh :3
amorfide
  • amorfide
well.. i get |dw:1352060900067:dw|
amorfide
  • amorfide
if i multiply by x/x will that give me the right answer?
amorfide
  • amorfide
@zepdrix
amorfide
  • amorfide
so how would i find the gradient of (4lnx-3)/(4lnx+3)
zepdrix
  • zepdrix
|dw:1352061081956:dw| Hmmm I'm confused how you get 24/x on the top :O
zepdrix
  • zepdrix
Nevermind I see it now XD
zepdrix
  • zepdrix
Me so slow today :3
amorfide
  • amorfide
i moved on, i need the gradient lol... how?
zepdrix
  • zepdrix
the gradient? :( mmm I'm in the US, is that what we call the slope i guess? :O
amorfide
  • amorfide
yeah slope
zepdrix
  • zepdrix
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.
amorfide
  • amorfide
crosses the x axis y=(4lnx-3)/(4lnx+3) get the exact value of the gradient
zepdrix
  • zepdrix
|dw:1352061602252:dw| Understand how we got that particular x value? It's a little bit tricky near the end there.
amorfide
  • amorfide
ahh thank you! forget to make it equal to zero my bad xD
zepdrix
  • zepdrix
Understand how to find the value of the gradient from there? :) Plugging that point into the derivative function and such? :D
amorfide
  • amorfide
36e^3/4 ?
amorfide
  • amorfide
ahh that is just the denominator my bad (2/3)e^(3/4)
amorfide
  • amorfide
that should be -3/4
zepdrix
  • zepdrix
|dw:1352062210018:dw| Hmm yah that looks right, good job! :)

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