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Math Help - Derivative of a particular function - help

  1. #1
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    Derivative of a particular function - help

    Hi,

    I have the following function:

    Code:
    h = k1 - k2
    a = (k1 - x) / h
    b = (x - k2) / h
    y = a * k3 + b * k4 + ((a^3 - a) * k5 + (b^3 - b) * k6) * (h^2) / 6
    I need to know the derivative of y regarding x.

    Can someone help me out?

    Sorry to bother.

    Kind regards,

    Kepler
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  2. #2
    A Plied Mathematician
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    What ideas have you had so far?
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  3. #3
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    Hi,

    Substitution; then writing the 3th degree equations in extense. Then calculate the derivative. But I'm afraid I might be lost in the process.

    Kind regards,

    Kepler
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  4. #4
    A Plied Mathematician
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    You could do it that way. Perhaps a more compact way would be not to substitute, but to regard a = a(x) and b = b(x), and use the chain rule. What does that give you?
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  5. #5
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    Hi again,

    I went with my method and it was a mess...
    The substitutiom gave:

    Code:
    y = ((k1-x)/h)*k3+((x-k2)/h)*k4+((((k1-x)/h)^3-((k1-x)/h))*k5+(((x-k2)/h)^3-((x-k2)/h))*k6)*(h^2)/6
    and I obtained the derivative:

    Code:
    y' = ((3*k6-3*k5)*x^2+(6*k1*k5-6*k2*k6)*x+(3*k2^2-h^2)*k6+(h^2-3*k1^2)*k5+6*k4-6*k3)/(6*h)
    Is this right? I'm not sure...

    Kind regards,

    Kepler
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  6. #6
    A Plied Mathematician
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    Looks good to me.
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  7. #7
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    Hi again,

    Sorry to ask Adrian - probably a dumb question: but did you check? It's very important that the formula is right.

    Sorry to bother you.

    Kind regards,

    Kepler
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  8. #8
    A Plied Mathematician
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    I wouldn't have said the answer looks right unless I had checked it. So yes, I did check it. However, you can check it, too, using WolframAlpha.
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  9. #9
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    Thanks again - I said it was a dumb question. You were very helpful. Thanks again.

    Kind regards,

    Kepler
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  10. #10
    A Plied Mathematician
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    You're welcome. Have a good one!
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