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El_Tucan
Group Title
what is the first step in finding the first derivative using logarithmic differentiation for y = (cos x)^(sin x)?
 one year ago
 one year ago
El_Tucan Group Title
what is the first step in finding the first derivative using logarithmic differentiation for y = (cos x)^(sin x)?
 one year ago
 one year ago

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phuchh1402 Group TitleBest ResponseYou've already chosen the best response.0
Isn't you have to move sin(x) like this => y = sin(x)ln(cos(x))?
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
almost, the first step is to just log each side
 one year ago

phuchh1402 Group TitleBest ResponseYou've already chosen the best response.0
yes, i know
 one year ago

electrokid Group TitleBest ResponseYou've already chosen the best response.0
\[y=(\cos x)^{\sin x}\] take a logarithm on the both sides
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
ln(y) = sin(x) ln(cos(x))
 one year ago

phuchh1402 Group TitleBest ResponseYou've already chosen the best response.0
then take derivative both side sin = cos and cos = sin
 one year ago

El_Tucan Group TitleBest ResponseYou've already chosen the best response.0
right right right! :)
 one year ago

El_Tucan Group TitleBest ResponseYou've already chosen the best response.0
just for referance
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
i think you dropped a negative on the ln cosx chain
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
\[sin(x)~ln(cos(x))\] \[cos(x)~ln(cos(x))+sin(x)~\frac{sin(x)}{cos(x)}\] \[cos(x)~ln(cos(x))sin^2(x)~\frac{1}{cos(x)}\]
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
or you might have just went another way to get to the same thing :)
 one year ago

amistre64 Group TitleBest ResponseYou've already chosen the best response.0
the end result looks fine tho.
 one year ago

El_Tucan Group TitleBest ResponseYou've already chosen the best response.0
thanks huh
 one year ago

El_Tucan Group TitleBest ResponseYou've already chosen the best response.0
:) i love open study
 one year ago
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