anonymous
  • anonymous
Derviative.
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
\[y = e ^{e ^{x}}\]
anonymous
  • anonymous
dy/dx=(e^e^x)(2e^x), is that right?
anonymous
  • anonymous
(2e^x) ?

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anonymous
  • anonymous
derivative of e, is e times what ever it is raised, so u get e^e^x times e^x
anonymous
  • anonymous
i mean,,, (e^e^x)(e^x)
anonymous
  • anonymous
\[ \huge f(x)= e ^{e ^{x}} \implies f'(x)=\huge e^{e^x+x} \]
anonymous
  • anonymous
how u get that foolformath?, is it a rule or ?
TuringTest
  • TuringTest
apply the chain rule\[\large g(x)=e^x\]\[\large f(x)=e^{g(x)}\to f'(x)=g'(x)e^{g(x)}=e^xe^{e^x}=e^{e^x+x}\]
anonymous
  • anonymous
I use more elementary things, say \[ \huge y= e ^{e ^{x}} \] Now, take logarithm (natural) of both sides, \[ \huge \ln y= e^x \implies \frac1y \frac {dy}{dx} = e^x \]\[\huge \implies \frac {dy}{dx} = e^{e^x+x} \]
anonymous
  • anonymous
I (now) think Turing's process is more more elementary, as mine use implicit differentiation.
TuringTest
  • TuringTest
yeah I didn't want to be contradictory...
TuringTest
  • TuringTest
yours is faster though
anonymous
  • anonymous
Yes, I have a proclivity to assume that fast is elementary, but you are one with simple yet beautiful answer always :)
TuringTest
  • TuringTest
cheers :)
anonymous
  • anonymous
:)

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