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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)?

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  1. phuchh1402
    • 3 years ago
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    Isn't you have to move sin(x) like this => y = sin(x)ln(cos(x))?

  2. amistre64
    • 3 years ago
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    almost, the first step is to just log each side

  3. phuchh1402
    • 3 years ago
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    yes, i know

  4. electrokid
    • 3 years ago
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    \[y=(\cos x)^{\sin x}\] take a logarithm on the both sides

  5. amistre64
    • 3 years ago
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    ln(y) = sin(x) ln(cos(x))

  6. phuchh1402
    • 3 years ago
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    then take derivative both side sin = cos and cos = -sin

  7. El_Tucan
    • 3 years ago
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    right right right! :)

  8. El_Tucan
    • 3 years ago
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    just for referance

  9. amistre64
    • 3 years ago
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    i think you dropped a negative on the ln cosx chain

  10. amistre64
    • 3 years ago
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    \[sin(x)~ln(cos(x))\] \[cos(x)~ln(cos(x))+sin(x)~\frac{-sin(x)}{cos(x)}\] \[cos(x)~ln(cos(x))-sin^2(x)~\frac{1}{cos(x)}\]

  11. amistre64
    • 3 years ago
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    or you might have just went another way to get to the same thing :)

  12. amistre64
    • 3 years ago
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    the end result looks fine tho.

  13. El_Tucan
    • 3 years ago
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    thanks huh

  14. El_Tucan
    • 3 years ago
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    :) i love open study

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