Question

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

Answer 1

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

Answer 2

almost, the first step is to just log each side

Answer 3

yes, i know

Answer 4

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

Answer 5

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

Answer 6

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

Answer 7

right right right! :)

Answer 8

just for referance

Answer 9

i think you dropped a negative on the ln cosx chain

Answer 10

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

Answer 11

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

Answer 12

the end result looks fine tho.

Answer 13

thanks huh

Answer 14

:) i love open study