PhoenixFire
  • PhoenixFire
How do you find the derivative of \[{cos(x)}^{cos(x)}\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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lgbasallote
  • lgbasallote
interesting
lgbasallote
  • lgbasallote
is x raised to cos x? or is cos x raised to cos x?
PhoenixFire
  • PhoenixFire
cos(x) raised to cos(x). \[(cos(x))^{cos(x)}\]

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anonymous
  • anonymous
Let y = ( cosx )^( cosx) Take ln both sides:...
PhoenixFire
  • PhoenixFire
\[y=(cos x)^{cos x}\] \[ln y=(cos x)(ln(cos x))\] differentiate both side with respect to x. \[LHS={1 \over y}{dy \over dx}\] RHS=product rule. then rearrange for dy/dx? Yeah?
anonymous
  • anonymous
Yupe :)
anonymous
  • anonymous
Actually, ( lny )' = y' / y
PhoenixFire
  • PhoenixFire
\[{dy \over dx}=-ysin x(ln(cos x) + 1)\] That doesn't seem right.
anonymous
  • anonymous
Then plug y = cosx ^ cosx back

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