zned6559
  • zned6559
what is the derivative of (sin(e))^x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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anonymous
  • anonymous
the deriv of sin(x) is cos(x) and solve as a chain rule
anonymous
  • anonymous
the derivative of e^x is e^x
zned6559
  • zned6559
the answer is ln(sin(e)) (sin(e))^x but how do you get to this

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TrojanPoem
  • TrojanPoem
@asong195 , The x isn't the power of e , but the whole thing.
TrojanPoem
  • TrojanPoem
assume you have y = u^v take ln for both sides lny = vlnu (derive) y'/y = v'lnu + v * u'/u y = u^v y' = u^v v' ln u + v * u^(v-1) * u'
TrojanPoem
  • TrojanPoem
You can use the last formula for deriving or add ln yourself.
TrojanPoem
  • TrojanPoem
y = (sin(e))^x ln y = x lnsin(e) (notice that lnsine is a constant) y'/y= lnsin(e) (from the main y) y' = ylnsin(e) = (sin(e))^x * lnsin(e)
zned6559
  • zned6559
how come you don't derive lnsin(e)

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