help me with math =/

Discussion in 'Random Topic Center' started by BlazeUp, Jan 23, 2008.

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  1. BlazeUp

    BlazeUp New Member

    i have no idea how to do this..

    If f'(x) = x^3 and u = e^x, show that d/dx(f(u)) = e^4x

    i dont evne know where to begin...
  2. Chairman Kaga

    Chairman Kaga Active Member

    Yay calculus.

    First (and you probably know this), f'(x) is shorthand for df/dx
    so if f'(x) = x^3
    then f(x) = (1/4)(x^4) (anti-derivative of x^3)

    So f(u) = f(e^x)
    = (1/4)((e^x)^4)
    = (1/4)(e^4x)​

    d/dx((1/4)(e^4x)) = (1/4) d/dx(e^4x) (Constant rule: If k is constant then d/dx(kx) = k(d/dx(x)))

    Now apply the chain rule to the new derivative:
    If h(x) = f(g(x))
    then h'(x) = f'(g(x)) g'(x)​
    f(x) = e^x​
    g(x) = 4x​
    Now derive:

    f(x) = e^x => f'(x)= e^x (e^x is its own derivative)

    g(x) = 4x => g'(x) = (4)(1x^0) = 4

    So h'(x) = (e^(4x))(4)
    = 4e^4x​

    So back to d/dx((1/4)(e^4x))
    = (1/4) d/dx(e^4x)
    = (1/4) (4e^4x)
    = (1/4) (4) (e^4x)
    = e^4x​

    I repeat: yay calculus.

    And I eagerly await a bulletin board that can handle MathML.

    Also, I take the title "Pokemon Professor" quite literally.
    Last edited: Jan 24, 2008
  3. bullados

    bullados <a href="

    Nothing more to add. Excellent explanation!
  4. Chairman Kaga

    Chairman Kaga Active Member

    And I told myself I'd never need this crap again.

    I was right. But I'm glad I could remember some of it :)
  5. ShadowTogetic

    ShadowTogetic New Member

    That's correct, pretty simple. You can teach an online course =D
  6. Dom

    Dom New Member

    lol weird. I've just been doing this exact same stuff this week. You guys use slightly different notations to us but its all the same in the end. math <3
  7. ZAKtheGeek

    ZAKtheGeek New Member

    Sheesh that's complicated. Why not just say d/dx(f(u)) = f'(u)u' = [(e^x)^3][e^x] = (e^3x)(e^x) = e^4x ?

    Also, technically, you should probably have a constant at the end of your integral. Even though you're just going to take the derivative immediately.
  8. Chairman Kaga

    Chairman Kaga Active Member

    Because I like complexity.
  9. Magic_Umbreon

    Magic_Umbreon Researching Tower Scientist, Retired

    I agree with ZAK, it's good practice to remember the c with it being the easiest to forget etc.
  10. Chairman Kaga

    Chairman Kaga Active Member

    Honestly, I just missed the fact I could use the chain rule on the original problem. No big deal, the proof still works ;)
  11. sean009

    sean009 New Member

    I just posted here to see whats going on in this thread.By the way till high standard i had not heard about this chain rule.Which standard do u read?
  12. pat460

    pat460 New Member

    No offense or anything, but why did you ask for math help on pokegym?
  13. Chairman Kaga

    Chairman Kaga Active Member

    It worked, didn't it?
  14. ~Blazi-King~

    ~Blazi-King~ New Member

    Because it was a Random "Topic!"

    On top of that, there are some VERY intelligent people on Pokegym, that have expertises is different areas...The above happened to be in "Math.":thumb:
  15. dogma

    dogma New Member

    The first explanation is good because it is far easier to use if the problem had more complicated derivatives... but yes, forgetting constants of integration is a big no-no :rolleyes:

    They give the same answer in the end - use the one you like best.
  16. ShadowTogetic

    ShadowTogetic New Member

  17. dogma

    dogma New Member

    fine, be pedantic :biggrin:
  18. mewlover777

    mewlover777 New Member

    click here...

    ^ Is that
    for you?

    I'm scared of this kind of stuff when I get to high school..I'm gonna be posting stuff like this on here alot :lol:

    P.S. is this random or what?

    the above link was so funny...
  19. Magic_Umbreon

    Magic_Umbreon Researching Tower Scientist, Retired

    I edited the quote below to fix your formatting to indeces instead of ^s:

  20. Chairman Kaga

    Chairman Kaga Active Member

    *hits self for not seeing there is a superscript vbcode*

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