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

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anonymous
 3 years 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
 3 years ago
Best ResponseYou've already chosen the best response.0almost, the first step is to just log each side

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

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

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0then take derivative both side sin = cos and cos = sin

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

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

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