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Math Help - Differentiate y = cos(a^3 + x^3)

  1. #1
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    Differentiate y = cos(a^3 + x^3)

    The problem is as follows: Differentiate y = cos(a^3 + x^3)

    my current solution:

    By the chain rule
    u = a^3 + x^3
    f(u) = cos(u)

    u' = 3a^2 + 3x^2 (by the power rule)
    f ' (u) = -sin(u)

    therefore,

    -sin(a^3 + x^3)(3a^2 + 3x^2) = -3a^2sin(a^3 + x^3) - 3x^2sin(a^3 + x^3)

    This is the solution I come up with, however it is incorrect and I don't know why.
    correct solution should be -3x^2sin(a^3 + x^3). Where is the -3a^2sin(a^3 + x^3)
    going?
    Last edited by mr fantastic; October 5th 2011 at 01:41 PM. Reason: Re-titled.
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  2. #2
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    Re: Plz help with a particular differentiation

    Quote Originally Posted by iAmKrizzle View Post
    By the chain rule
    u = a^3 + x^3
    f(u) = cos(u)

    u' = 3a^2 + 3x^2 (by the power rule)
    This is not correct, i'm guessing you are only differentiating w.r.t x?
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  3. #3
    Super Member Quacky's Avatar
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    Re: Plz help with a particular differentiation

    You are almost right. Your mistake comes from forgetting that a^3 is not a variable: it's a constant value, such as 8 or 27. Therefore when we differentiate it, we just get 0 - it vanishes!

    y=cos(a^3+x^3)

    Let u=a^3+x^3

    \frac{du}{dx}=3x^2

    \frac{dy}{du}=-sin(u)

    \frac{dy}{dx}=\frac{dy}{du}\cdot\frac{du}{dx}
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  4. #4
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    Re: Plz help with a particular differentiation

    thank you Quacky that makes sense. I was treating a^3 as a variable. Thank you for your help.
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