PhoenixFire
How do you find the derivative of
\[{cos(x)}^{cos(x)}\]
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lgbasallote
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interesting
lgbasallote
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is x raised to cos x? or is cos x raised to cos x?
PhoenixFire
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cos(x) raised to cos(x).
\[(cos(x))^{cos(x)}\]
Chlorophyll
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Let y = ( cosx )^( cosx)
Take ln both sides:...
PhoenixFire
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\[y=(cos x)^{cos x}\]
\[ln y=(cos x)(ln(cos x))\]
differentiate both side with respect to x.
\[LHS={1 \over y}{dy \over dx}\]
RHS=product rule. then rearrange for dy/dx? Yeah?
Chlorophyll
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Yupe :)
Chlorophyll
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Actually,
( lny )' = y' / y
PhoenixFire
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\[{dy \over dx}=-ysin x(ln(cos x) + 1)\]
That doesn't seem right.
Chlorophyll
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Then plug y = cosx ^ cosx back