amorfide
Differentiate step by step I don't remember how to do it
(4lnx-3)/(4lnx+3)
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amorfide
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would i do (vdu-udv)/v²
amorfide
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@cwrw238
amorfide
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@Hero can you help?
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.
amorfide
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no do it straight off use substitute v and u if needed
amorfide
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actually i do not think method matters xD
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 :)
amorfide
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i am sure it is quotient,...
zepdrix
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Oh i didn't see the division symbol in there sorry, it was hidden for some reason lolol
amorfide
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i have the answer no method
answer is
24/x(4lnx+3)²
zepdrix
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I hate that tiny text :)
zepdrix
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k you have the right formula then, just need help setting it up? :o
amorfide
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well i know which is v and u i dont know the differential of 4lnx -3
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.
amorfide
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I feel dumb, thank you <3
zepdrix
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heh :3
amorfide
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well.. i get
|dw:1352060900067:dw|
amorfide
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if i multiply by x/x will that give me the right answer?
amorfide
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@zepdrix
amorfide
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so how would i find the gradient of (4lnx-3)/(4lnx+3)
zepdrix
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|dw:1352061081956:dw|
Hmmm I'm confused how you get 24/x on the top :O
zepdrix
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Nevermind I see it now XD
zepdrix
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Me so slow today :3
amorfide
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i moved on, i need the gradient lol... how?
zepdrix
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the gradient? :( mmm I'm in the US, is that what we call the slope i guess? :O
amorfide
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yeah slope
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.
amorfide
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crosses the x axis
y=(4lnx-3)/(4lnx+3)
get the exact value of the gradient
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.
amorfide
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ahh thank you! forget to make it equal to zero my bad xD
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
amorfide
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36e^3/4 ?
amorfide
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ahh that is just the denominator my bad
(2/3)e^(3/4)
amorfide
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that should be -3/4
zepdrix
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|dw:1352062210018:dw|
Hmm yah that looks right, good job! :)