El_Tucan
  • El_Tucan
what is the first step in finding the first derivative using logarithmic differentiation for y = (cos x)^(sin x)?
Calculus1
chestercat
  • chestercat
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anonymous
  • anonymous
Isn't you have to move sin(x) like this => y = sin(x)ln(cos(x))?
amistre64
  • amistre64
almost, the first step is to just log each side
anonymous
  • anonymous
yes, i know

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anonymous
  • anonymous
\[y=(\cos x)^{\sin x}\] take a logarithm on the both sides
amistre64
  • amistre64
ln(y) = sin(x) ln(cos(x))
anonymous
  • anonymous
then take derivative both side sin = cos and cos = -sin
El_Tucan
  • El_Tucan
right right right! :)
El_Tucan
  • El_Tucan
just for referance
amistre64
  • amistre64
i think you dropped a negative on the ln cosx chain
amistre64
  • amistre64
\[sin(x)~ln(cos(x))\] \[cos(x)~ln(cos(x))+sin(x)~\frac{-sin(x)}{cos(x)}\] \[cos(x)~ln(cos(x))-sin^2(x)~\frac{1}{cos(x)}\]
amistre64
  • amistre64
or you might have just went another way to get to the same thing :)
amistre64
  • amistre64
the end result looks fine tho.
El_Tucan
  • El_Tucan
thanks huh
El_Tucan
  • El_Tucan
:) i love open study

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