amyna
  • amyna
Find the derivative: f(x)=ln (lnx) Help!! i don't know where to start!! Do i use product rule?
Mathematics
  • Stacey Warren - Expert brainly.com
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chestercat
  • chestercat
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jim_thompson5910
  • jim_thompson5910
you'll use the chain rule actually
jim_thompson5910
  • jim_thompson5910
have you learned that rule?
jim_thompson5910
  • jim_thompson5910
|dw:1441070107450:dw|

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jim_thompson5910
  • jim_thompson5910
|dw:1441070124683:dw|
jim_thompson5910
  • jim_thompson5910
|dw:1441070149590:dw|
jim_thompson5910
  • jim_thompson5910
so f(x) = Ln(x) g(x) = Ln(x) h(x) = f(g(x)) = Ln(Ln(x))
jim_thompson5910
  • jim_thompson5910
hopefully that helps?
amyna
  • amyna
can anyone show all the steps? I'm still a little confused...
jim_thompson5910
  • jim_thompson5910
if we had f(x) = Ln(x), what would be the derivative?
amyna
  • amyna
1/x
jim_thompson5910
  • jim_thompson5910
yes, now what we do is replace the 'x' with Ln(x) |dw:1441070946608:dw|
jim_thompson5910
  • jim_thompson5910
or put another way, we replace x with g(x) = Ln(x)
jim_thompson5910
  • jim_thompson5910
and then we multiply by the derivative of the inside we multiply by g ' (x)
jim_thompson5910
  • jim_thompson5910
g(x) = Ln(x) g ' (x) = 1/x |dw:1441071005586:dw|
amyna
  • amyna
ok got it!! thanks so much!!
jim_thompson5910
  • jim_thompson5910
here's a page with tons of chain rule practice problems https://www.math.ucdavis.edu/~kouba/CalcOneDIRECTORY/chainruledirectory/ChainRule.html they have detailed solutions to help explain and help you practice more
amyna
  • amyna
Thanks! :)
jim_thompson5910
  • jim_thompson5910
no problem

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