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lovesit2x Group Title

Differentiate y = e^(4x) cos x with respect to x dy/dx = ?

  • one year ago
  • one year ago

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  1. zepdrix Group Title
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    Hmm looks like we'll have to apply the product rule :)

    • one year ago
  2. Xavier Group Title
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    You have a product so use the product rule

    • one year ago
  3. zepdrix Group Title
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    \[\large y=e^{4x}\cos x\]\[\large y'=\color{royalblue}{\left(e^{4x}\right)'}\cos x+e^{4x}\color{royalblue}{\left(\cos x\right)'}\] Understand the setup for Product Rule? We have to take the derivative of the blue terms.

    • one year ago
  4. lovesit2x Group Title
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    Yes

    • one year ago
  5. zepdrix Group Title
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    So what's the derivative of cos x? :)

    • one year ago
  6. lovesit2x Group Title
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    sin x ?

    • one year ago
  7. lovesit2x Group Title
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    wait -sinx

    • one year ago
  8. zepdrix Group Title
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    Yes good c:\[\large y'=\color{royalblue}{\left(e^{4x}\right)'}\cos x+e^{4x}\left(-\sin x\right)\]

    • one year ago
  9. zepdrix Group Title
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    Do you remember the derivative of \(\huge e^x\) ?

    • one year ago
  10. lovesit2x Group Title
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    Nope :)

    • one year ago
  11. zepdrix Group Title
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    Oooo tsk tsk! That's a fun easy one that you'll want to remember! c: \[\huge \left(e^x\right)'=e^x\] It gives us the same thing back. This same thing will happen in our problem here, except we'll have an extra step. Since our exponent is more than just \(\large x\), we have to apply the chain rule. Multiply the result by the derivative of the exponent. \[\huge \left(e^{4x}\right)'=e^{4x}\left(4x\right)'\]

    • one year ago
  12. zepdrix Group Title
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    Hmm so what is the derivative of that exponent. The derivative of \(\large 4x\).... hmmmm

    • one year ago
  13. lovesit2x Group Title
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    4x

    • one year ago
  14. zepdrix Group Title
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    The derivative of 4x is 4x? Hmm no that's not going to work :c

    • one year ago
  15. lovesit2x Group Title
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    4

    • one year ago
  16. lovesit2x Group Title
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    lol

    • one year ago
  17. zepdrix Group Title
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    Yessss good :) Giving us, \(\huge e^{4x}(4)\) Which gives us an answer of,\[\huge y'=4e^{4x}\cos x+e^{4x}\left(-\sin x\right)\]

    • one year ago
  18. lovesit2x Group Title
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    WOW...you just made math fun. lol Thanks

    • one year ago
  19. zepdrix Group Title
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    lol :3 np

    • one year ago
  20. lovesit2x Group Title
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    wait...its with respect to x

    • one year ago
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