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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. anonymous

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

2. amistre64

almost, the first step is to just log each side

3. anonymous

yes, i know

4. anonymous

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

5. amistre64

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

6. anonymous

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

7. El_Tucan

right right right! :)

8. El_Tucan

just for referance

9. amistre64

i think you dropped a negative on the ln cosx chain

10. amistre64

$sin(x)~ln(cos(x))$ $cos(x)~ln(cos(x))+sin(x)~\frac{-sin(x)}{cos(x)}$ $cos(x)~ln(cos(x))-sin^2(x)~\frac{1}{cos(x)}$

11. amistre64

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

12. amistre64

the end result looks fine tho.

13. El_Tucan

thanks huh

14. El_Tucan

:) i love open study

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