anonymous
  • anonymous
find f'(x) if f(x) = ln(sinx)
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
derivative of sinx divided by sinx
anonymous
  • anonymous
\[\frac{d}{dx}[\ln(f(x))]=\frac{f'(x)}{f(x)}\] via the chain rule
anonymous
  • anonymous
oops

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anonymous
  • anonymous
cotx
anonymous
  • anonymous
f(x) = ln(sinx) y' = (1/sinx)(cosx) y' = cosx/sinx y' = cotx
anonymous
  • anonymous
f'(x)=d(lnsinx)/dx = {d(ln sinx) /dsinx} * {dsinx /dx} ={1/sinx} *{cosx} =cosx/sinx =cotx
anonymous
  • anonymous
got it?
lgbasallote
  • lgbasallote
oops? @satellite73
anonymous
  • anonymous
why cot x and not tan x
anonymous
  • anonymous
there was an erroneous tangent floating around, it is gone
anonymous
  • anonymous
oh look, it came back!!
anonymous
  • anonymous
U can write it interms of tan x too
anonymous
  • anonymous
BUT: f'(x)= 1/tan x
anonymous
  • anonymous
thanks

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