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anonymous

  • one year ago

How do you apply the power rule when E is raised by an power to a power? f[x] = e^(x^2) f'[x] = ???

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  1. TheSmartOne
    • one year ago
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    @Michele_Laino QH help :)

  2. amistre64
    • one year ago
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    derivative or integration?

  3. mathstudent55
    • one year ago
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    You don;t use the power rule here. Here you need the derivative of e^u, where u is a function in x.

  4. amistre64
    • one year ago
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    i see, derivative, chain and then power

  5. anonymous
    • one year ago
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    trying to get to derivative.. yes

  6. mathstudent55
    • one year ago
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    \(\dfrac{d}{dx} e^u = e^u \dfrac{d}{dx}u\)

  7. Michele_Laino
    • one year ago
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    here we have to apply the derivation of composed functions

  8. mathstudent55
    • one year ago
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    Oh, I see. The power rule does come in to differentiate the exponent, x^2.

  9. anonymous
    • one year ago
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    so its like 2 functions?

  10. Michele_Laino
    • one year ago
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    noe we can write your function as follows: \[f\left( x \right) = {e^{g\left( x \right)}},\quad g\left( x \right) = {x^2}\]

  11. Michele_Laino
    • one year ago
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    so the requested first derivative is given by the subsequent formula: \[f'\left( x \right) = \frac{{df}}{{dg}} \times \frac{{dg}}{{dx}} = {e^{g\left( x \right)}} \times 2x = 2x{e^{{x^2}}}\]

  12. anonymous
    • one year ago
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    wicked .. thank you now I just need to get my head around that.. :) ... first day solving derivative problems using rules. .. :)

  13. Michele_Laino
    • one year ago
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    thank you! :)

  14. anonymous
    • one year ago
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    makes sense though :)

  15. Michele_Laino
    • one year ago
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    need more help?

  16. anonymous
    • one year ago
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    all good thnx

  17. Michele_Laino
    • one year ago
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    thanks!! :)

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