Maths c4 differentiation

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  1. sabre2th1's Avatar
    1 04-06-2012  13:40
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    Maths c4 differentiation


    after differentiating x3, you get 3x2, why don't you write down dx/dy next to it? (like is done with the others..).. I remember vaguely that it cancels or something?
  2. tommm's Avatar
    2 04-06-2012  13:42
    • Banned
    Re: Maths c4 differentiation
    You're differentiating each term with respect to x. If the term is just a function of x, this means you just differentiate it normally, as nothing you're doing has anything to do with y.
  3. TenOfThem's Avatar
    3 04-06-2012  13:53
    • TSR Royalty
    Re: Maths c4 differentiation
    \frac{d}{dx}(x^3) = 3x^2

    Whereas

    \frac{d}{dx}(y^3) = \frac{d}{dy}(y^3) \times \frac{dy}{dx} = 3y^2\frac{dy}{dx}



    Sorry about the typo
    Last edited by TenOfThem; 04-06-2012 at 16:07. Reason: ooops
  4. sabre2th1's Avatar
    4 04-06-2012  13:57
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    Re: Maths c4 differentiation
    (Original post by TenOfThem)
    \frac{d}{dx}(x^3) = 3x^2

    Whereas

    \frac{d}{dx}(y^2) = \frac{d}{dy}(y^3) \times \frac{dy}{dx} = 3y^2\frac{dy}{dx}
    Thanks, but I am confused , where did the y squared come from?
  5. TenOfThem's Avatar
    5 04-06-2012  14:12
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    Re: Maths c4 differentiation
    (Original post by sabre2th1)
    Thanks, but I am confused , where did the y squared come from?
    If you know where the x^2 came from why don't you know where the y^2 came from
  6. F1Addict's Avatar
    6 04-06-2012  14:17
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    Re: Maths c4 differentiation
    The dy/dx comes from the chain rule:
    \dfrac{d (f(y))}{dx} = \dfrac{d (f(y))}{dy} \dfrac{dy}{dx}

    where f(y) is a function of y. If f(y) is y^3 then it becomes what TenOfThem posted.
    Last edited by F1Addict; 04-06-2012 at 14:19.
  7. delllboy's Avatar
    7 04-06-2012  15:55
    • Exalted Member
    • Posts: 339
    Re: Maths c4 differentiation
    (Original post by TenOfThem)
    \frac{d}{dx}(x^3) = 3x^2

    Whereas

    \frac{d}{dx}(y^2) = \frac{d}{dy}(y^3) \times \frac{dy}{dx} = 3y^2\frac{dy}{dx}
    differentiating y^2 doesn't give you 3y^2 which is what is confusing.
  8. TenOfThem's Avatar
    8 04-06-2012  16:06
    • TSR Royalty
    Re: Maths c4 differentiation
    (Original post by delllboy)
    differentiating y^2 doesn't give you 3y^2 which is what is confusing.
    Thanks ... I had it in the second bracket with an error in the first


    Corrected now
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