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

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lgbasallote
 4 years ago
Best ResponseYou've already chosen the best response.0is x raised to cos x? or is cos x raised to cos x?

PhoenixFire
 4 years ago
Best ResponseYou've already chosen the best response.0cos(x) raised to cos(x). \[(cos(x))^{cos(x)}\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Let y = ( cosx )^( cosx) Take ln both sides:...

PhoenixFire
 4 years ago
Best ResponseYou've already chosen the best response.0\[y=(cos x)^{cos x}\] \[ln y=(cos x)(ln(cos x))\] differentiate both side with respect to x. \[LHS={1 \over y}{dy \over dx}\] RHS=product rule. then rearrange for dy/dx? Yeah?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Actually, ( lny )' = y' / y

PhoenixFire
 4 years ago
Best ResponseYou've already chosen the best response.0\[{dy \over dx}=ysin x(ln(cos x) + 1)\] That doesn't seem right.

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0Then plug y = cosx ^ cosx back
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