Question

How do you find the derivative of
\[{cos(x)}^{cos(x)}\]

Answer 1

interesting

Answer 2

is x raised to cos x? or is cos x raised to cos x?

Answer 3

cos(x) raised to cos(x).
\[(cos(x))^{cos(x)}\]

Answer 4

Let y = ( cosx )^( cosx)
Take ln both sides:...

Answer 5

\[y=(cos x)^{cos x}\]
\[ln y=(cos x)(ln(cos x))\]
differentiate both side with respect to x.
\[LHS={1 \over y}{dy \over dx}\]
RHS=product rule. then rearrange for dy/dx? Yeah?

Answer 6

Yupe :)

Answer 7

Actually,
( lny )' = y' / y

Answer 8

\[{dy \over dx}=-ysin x(ln(cos x) + 1)\]
That doesn't seem right.

Answer 9

Then plug y = cosx ^ cosx back