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



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phuchh1402
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Isn't you have to move sin(x) like this => y = sin(x)ln(cos(x))?

amistre64
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almost, the first step is to just log each side

phuchh1402
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yes, i know

electrokid
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\[y=(\cos x)^{\sin x}\]
take a logarithm on the both sides

amistre64
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ln(y) = sin(x) ln(cos(x))

phuchh1402
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then take derivative both side sin = cos and cos = sin

El_Tucan
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right right right! :)

El_Tucan
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just for referance

amistre64
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i think you dropped a negative on the ln cosx chain

amistre64
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\[sin(x)~ln(cos(x))\]
\[cos(x)~ln(cos(x))+sin(x)~\frac{sin(x)}{cos(x)}\]
\[cos(x)~ln(cos(x))sin^2(x)~\frac{1}{cos(x)}\]

amistre64
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or you might have just went another way to get to the same thing :)

amistre64
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the end result looks fine tho.

El_Tucan
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thanks huh

El_Tucan
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:) i love open study