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 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
what is the first step in finding the first derivative using logarithmic differentiation for y = (cos x)^(sin x)?

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

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

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

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

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

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

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

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

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

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