Question

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

Answer 1

would i do (vdu-udv)/v²

Answer 2

@cwrw238

Answer 3

@Hero can you help?

Answer 4

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.

Answer 5

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

Answer 6

actually i do not think method matters xD

Answer 7

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 :)

Answer 8

i am sure it is quotient,...

Answer 9

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

Answer 10

i have the answer no method
answer is

24/x(4lnx+3)²

Answer 11

I hate that tiny text :)

Answer 12

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

Answer 13

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

Answer 14

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.

Answer 15

I feel dumb, thank you <3

Answer 16

heh :3

Answer 17

well.. i get

Answer 18

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

Answer 19

@zepdrix

Answer 20

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

Answer 21

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