- amorfide

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

- katieb

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- amorfide

would i do (vdu-udv)/v²

- amorfide

- amorfide

@Hero can you help?

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## More answers

- 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

no do it straight off use substitute v and u if needed

- amorfide

actually i do not think method matters xD

- 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

i am sure it is quotient,...

- zepdrix

Oh i didn't see the division symbol in there sorry, it was hidden for some reason lolol

- amorfide

i have the answer no method
answer is
24/x(4lnx+3)²

- zepdrix

I hate that tiny text :)

- zepdrix

k you have the right formula then, just need help setting it up? :o

- amorfide

well i know which is v and u i dont know the differential of 4lnx -3

- 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

I feel dumb, thank you <3

- zepdrix

heh :3

- amorfide

well.. i get
|dw:1352060900067:dw|

- amorfide

if i multiply by x/x will that give me the right answer?

- amorfide

- amorfide

so how would i find the gradient of (4lnx-3)/(4lnx+3)

- zepdrix

|dw:1352061081956:dw|
Hmmm I'm confused how you get 24/x on the top :O

- zepdrix

Nevermind I see it now XD

- zepdrix

Me so slow today :3

- amorfide

i moved on, i need the gradient lol... how?

- zepdrix

the gradient? :( mmm I'm in the US, is that what we call the slope i guess? :O

- amorfide

yeah slope

- 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

crosses the x axis
y=(4lnx-3)/(4lnx+3)
get the exact value of the gradient

- zepdrix

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

- amorfide

ahh thank you! forget to make it equal to zero my bad xD

- zepdrix

Understand how to find the value of the gradient from there? :)
Plugging that point into the derivative function and such? :D

- amorfide

36e^3/4 ?

- amorfide

ahh that is just the denominator my bad
(2/3)e^(3/4)

- amorfide

that should be -3/4

- zepdrix

|dw:1352062210018:dw|
Hmm yah that looks right, good job! :)

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