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lovesit2x

  • 3 years ago

Find (d^(2)y)/(dx^(2)) for the following function. y=e^(-4x^(2))

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  1. abb0t
    • 3 years ago
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    So find the second derivative of the function.

  2. abb0t
    • 3 years ago
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    This requires that you use the chain rule.

  3. lovesit2x
    • 3 years ago
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    \[Find \frac{ d ^{2}y }{ dx ^{2} } for the following function. y=e ^{-4x ^{2}}\]

  4. abb0t
    • 3 years ago
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    First, start by using chain rule. For the second derivative, you will be using product rule AND chain rule.

  5. Xavier
    • 3 years ago
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    You want \[\frac{d}{dx}\left( \frac{dy}{dx}\right)\]

  6. anonymous
    • 3 years ago
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    first derivative is \[-8xe^{-4x^2}\] by the chain rule second derivative requires the product rule

  7. zepdrix
    • 3 years ago
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    Do you understand how Sat got that first derivative? c:

  8. abb0t
    • 3 years ago
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    Yes. I do.

  9. lovesit2x
    • 3 years ago
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    yes

  10. zepdrix
    • 3 years ago
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    \[\large y'=-8xe^{-4x^2}\] So now you need to find the second derivative as was stated above. \(\large y''\) To differentiate this a second time, you'll need to apply the Product Rule, very similarly to the way we did it in the last problem! :)

  11. zepdrix
    • 3 years ago
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    Fine fine fine D: I'll do the pretty colors like last time. Maybe that will help.

  12. lovesit2x
    • 3 years ago
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    lol

  13. zepdrix
    • 3 years ago
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    \[\huge y''=\color{royalblue}{\left(-8x\right)'}e^{-4x^2}-8x\color{royalblue}{\left(e^{-4x^2}\right)'}\]Product Rule setup for the second derivative. The second blue term should give you the same thing you got for the first derivative!

  14. lovesit2x
    • 3 years ago
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    omg, its that easy??? why am i overthinking this

  15. zepdrix
    • 3 years ago
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    :3

  16. zepdrix
    • 3 years ago
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    What do you get for the first set of blue brackets?

  17. lovesit2x
    • 3 years ago
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    -8

  18. lovesit2x
    • 3 years ago
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    n the second is the -8x e ^-4x^2

  19. zepdrix
    • 3 years ago
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    \[\huge y''=\color{orangered}{\left(-8\right)}e^{-4x^2}-8x\color{orangered}{\left(-8xe^{-4x^2}\right)}\] Like that? Yay good job!

  20. lovesit2x
    • 3 years ago
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    i love that lol

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