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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
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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phuchh1402Best 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

amistre64Best ResponseYou've already chosen the best response.0
almost, the first step is to just log each side
 one year ago

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

amistre64Best ResponseYou've already chosen the best response.0
ln(y) = sin(x) ln(cos(x))
 one year ago

phuchh1402Best ResponseYou've already chosen the best response.0
then take derivative both side sin = cos and cos = sin
 one year ago

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

amistre64Best ResponseYou've already chosen the best response.0
i think you dropped a negative on the ln cosx chain
 one year ago

amistre64Best 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

amistre64Best 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

amistre64Best ResponseYou've already chosen the best response.0
the end result looks fine tho.
 one year ago
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