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

Question

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

anonymous · Answer

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

amistre64 · Answer

almost, the first step is to just log each side

anonymous · Answer

yes, i know

anonymous · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

el_tucan · Answer

right right right! :)

el_tucan · Answer

just for referance

amistre64 · Answer

i think you dropped a negative on the ln cosx chain

amistre64 · Answer

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

amistre64 · Answer

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

amistre64 · Answer

the end result looks fine tho.

el_tucan · Answer

thanks huh

el_tucan · Answer

:)  i love open study