anonymous
  • anonymous
How do you apply the power rule when E is raised by an power to a power? f[x] = e^(x^2) f'[x] = ???
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
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TheSmartOne
  • TheSmartOne
@Michele_Laino QH help :)
amistre64
  • amistre64
derivative or integration?
mathstudent55
  • mathstudent55
You don;t use the power rule here. Here you need the derivative of e^u, where u is a function in x.

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amistre64
  • amistre64
i see, derivative, chain and then power
anonymous
  • anonymous
trying to get to derivative.. yes
mathstudent55
  • mathstudent55
\(\dfrac{d}{dx} e^u = e^u \dfrac{d}{dx}u\)
Michele_Laino
  • Michele_Laino
here we have to apply the derivation of composed functions
mathstudent55
  • mathstudent55
Oh, I see. The power rule does come in to differentiate the exponent, x^2.
anonymous
  • anonymous
so its like 2 functions?
Michele_Laino
  • Michele_Laino
noe we can write your function as follows: \[f\left( x \right) = {e^{g\left( x \right)}},\quad g\left( x \right) = {x^2}\]
Michele_Laino
  • Michele_Laino
so the requested first derivative is given by the subsequent formula: \[f'\left( x \right) = \frac{{df}}{{dg}} \times \frac{{dg}}{{dx}} = {e^{g\left( x \right)}} \times 2x = 2x{e^{{x^2}}}\]
anonymous
  • anonymous
wicked .. thank you now I just need to get my head around that.. :) ... first day solving derivative problems using rules. .. :)
Michele_Laino
  • Michele_Laino
thank you! :)
anonymous
  • anonymous
makes sense though :)
Michele_Laino
  • Michele_Laino
need more help?
anonymous
  • anonymous
all good thnx
Michele_Laino
  • Michele_Laino
thanks!! :)

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