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lilg132

differentiate

  • one year ago
  • one year ago

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  1. lilg132
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    \[M = 4.2e ^{2x} - 2.9e ^{-0.2x}\]

    • one year ago
  2. mathdood
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    okay well what is the derivative of e^x?

    • one year ago
  3. lilg132
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    xe? i dont know

    • one year ago
  4. mathdood
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    it is e^x*x' and the derivative of x is 1 so you have e^x but in this case since you have 2x and -0.2x you need to bring those down and differentiate you know what I mean?

    • one year ago
  5. mathdood
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    crazy eh derivative of e^x is e^x!!

    • one year ago
  6. lilg132
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    LOL

    • one year ago
  7. lilg132
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    no i dont explain further please :(

    • one year ago
  8. mathdood
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    but that it isn't the end of your problem okay do you know how to take simple derivative like x^2? like do you know the power rule?

    • one year ago
  9. lilg132
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    x^2 would be 2x?

    • one year ago
  10. mathdood
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    right just making sure.

    • one year ago
  11. mathdood
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    Okay so when you see e^x you have e^x and when you see e^2x you get e^2x*(2x)' the ' means derivative. You understand? If not I don't mind continuing at all.

    • one year ago
  12. lilg132
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    ok.. e^2x * (2x)' is e^2x

    • one year ago
  13. mathdood
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    no what is the derivative of 2x?

    • one year ago
  14. lilg132
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    x^2 ?

    • one year ago
  15. lilg132
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    mindboggling

    • one year ago
  16. mathdood
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    no that is the integral of 2x think about it like this. The derivative is the rate of change of the function so you are looking for the how fast the function is changing. so how fast is 2x changing?

    • one year ago
  17. mathdood
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    sorry not how fast but by how much is it changing for each value of x

    • one year ago
  18. lilg132
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    2?

    • one year ago
  19. lilg132
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    by 2?

    • one year ago
  20. mathdood
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    yes =) just for fun what is the derivative of 2?

    • one year ago
  21. lilg132
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    LOL erm not sure

    • one year ago
  22. lilg132
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    1?

    • one year ago
  23. lilg132
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    wait its a constant

    • one year ago
  24. lilg132
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    so 0

    • one year ago
  25. mathdood
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    sorry I know I am dragging this out I just want to help you understand. Well think how much is the function y=2 changing over time right!! =)

    • one year ago
  26. mathdood
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    0

    • one year ago
  27. mathdood
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    Anyway back to the problem

    • one year ago
  28. lilg132
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    ok :)

    • one year ago
  29. mathdood
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    so if (e^2x)' = 2e^2x then what do you think (4.2e^2x)' = ?

    • one year ago
  30. lilg132
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    8.4e^2x

    • one year ago
  31. lilg132
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    please be right

    • one year ago
  32. mathdood
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    good stuff dude now how about (−2.9e^(−0.2x))' = ?

    • one year ago
  33. mathdood
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    yes you got it =) keep going you can do this

    • one year ago
  34. lilg132
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    :D 0.58e^-0.2x?

    • one year ago
  35. mathdood
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    I didn't check on the calculator but it looks right dude so now you just have to put the whole thing together you want to show me what that looks like?

    • one year ago
  36. lilg132
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    ok one second :D

    • one year ago
  37. lilg132
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    dm/dx = 8.4e^2x + 0.58e^-0.2x

    • one year ago
  38. mathdood
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    awesome dude high five! =)

    • one year ago
  39. lilg132
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    woooooooooooo !!!

    • one year ago
  40. lilg132
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    thanks alot mate appreciate it

    • one year ago
  41. mathdood
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    not a problem =) thanks

    • one year ago
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