Author 
Topic 

markmil2002
Average Member
USA
11 Posts 
Posted  09/17/2007 : 19:19:19

I'm trying to find the derivitive of f(x) = (x + 1)/(ln x)
After doing some math I got 2x/x but I don't think that is correct.



sahsjing
Advanced Member
USA
2399 Posts 
Posted  09/17/2007 : 20:27:52

You should have 1/(lnx) as a factor. Try it again? 


Subhotosh Khan
Advanced Member
USA
9116 Posts 
Posted  09/18/2007 : 09:26:27

quote: Originally posted by markmil2002
I'm trying to find the derivitive of f(x) = (x + 1)/(ln x)
After doing some math I got 2x/x but I don't think that is correct.
f(x) = u(x)/v(x)
df/dx = (u'*v  v'*u)/v^{2}.................(1)
In your case:
u(x) = x^{2} + 1 .................... u' = 2x
v(x) = ln(x) ................................ v' = 1/x
Using these in (1)
df/dx = [(2x) * ln(x)  (x^{2} + 1) * (1/x)]/{ln(x)}^{2}
Now simplify and continue... 


markmil2002
Average Member
USA
11 Posts 
Posted  09/18/2007 : 22:12:33

I've made it that far, but I dont see how to simplify. Obviously e will probably be involved to cancel ln, but I cant figure out how to apply it.
quote: Originally posted by Subhotosh Khan
quote: Originally posted by markmil2002
I'm trying to find the derivitive of f(x) = (x + 1)/(ln x)
After doing some math I got 2x/x but I don't think that is correct.
f(x) = u(x)/v(x)
df/dx = (u'*v  v'*u)/v^{2}.................(1)
In your case:
u(x) = x^{2} + 1 .................... u' = 2x
v(x) = ln(x) ................................ v' = 1/x
Using these in (1)
df/dx = [(2x) * ln(x)  (x^{2} + 1) * (1/x)]/{ln(x)}^{2}
Now simplify and continue...




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