## amorfide Group Title Differentiate step by step I don't remember how to do it (4lnx-3)/(4lnx+3) one year ago one year ago

1. amorfide Group Title

would i do (vdu-udv)/v²

2. amorfide Group Title

@cwrw238

3. amorfide Group Title

@Hero can you help?

4. zepdrix Group Title

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 Group Title

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

6. amorfide Group Title

actually i do not think method matters xD

7. zepdrix Group Title

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 Group Title

i am sure it is quotient,...

9. zepdrix Group Title

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

10. amorfide Group Title

11. zepdrix Group Title

I hate that tiny text :)

12. zepdrix Group Title

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

13. amorfide Group Title

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

14. zepdrix Group Title

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 Group Title

I feel dumb, thank you <3

16. zepdrix Group Title

heh :3

17. amorfide Group Title

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

18. amorfide Group Title

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

19. amorfide Group Title

@zepdrix

20. amorfide Group Title

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

21. zepdrix Group Title

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

22. zepdrix Group Title

Nevermind I see it now XD

23. zepdrix Group Title

Me so slow today :3

24. amorfide Group Title

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

25. zepdrix Group Title

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

26. amorfide Group Title

yeah slope

27. zepdrix Group Title

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 Group Title

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

29. zepdrix Group Title

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

30. amorfide Group Title

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

31. zepdrix Group Title

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

32. amorfide Group Title

36e^3/4 ?

33. amorfide Group Title

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

34. amorfide Group Title

that should be -3/4

35. zepdrix Group Title

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