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Math Help - Derivative

  1. #1
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    Derivative

    How do i find the derivative of the following? I'm having trouble on what kind of rule to use.

    f(x)=5/(x^3) - 3/(2-7x) + 3x^5 - 15 (Quotient rule?)



    g(x) = tan(x)ln(2x+5) (product rule?)


    y=cos(3-2x^4) (chain Rule??)


    thanks for your help
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by tim_mannire View Post
    How do i find the derivative of the following? I'm having trouble on what kind of rule to use.

    f(x)=5/(x^3) - 3/(2-7x) + 3x^5 - 15 (Quotient rule?)
    the derivative of a sum is the sum of derivatives. Then the power rule and chainrule.

    g(x) = tan(x)ln(2x+5) (product rule?)
    product rule and chain rule


    y=cos(3-2x^4) (chain Rule??)
    chain rule

    CB
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  3. #3
    MHF Contributor
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    Just in case a picture helps...

    Quote Originally Posted by CaptainBlack View Post
    Quote Originally Posted by tim_mannire View Post
    How do i find the derivative of the following? I'm having trouble on what kind of rule to use.

    f(x)=5/(x^3) - 3/(2-7x) + 3x^5 - 15 (Quotient rule?)
    the derivative of a sum is the sum of derivatives. Then the power rule and chainrule.


    Quote Originally Posted by tim_mannire View Post
    g(x) = tan(x)ln(2x+5) (product rule?)
    product rule and chain rule


    ... or, zooming in further...



    Quote Originally Posted by tim_mannire View Post
    y=cos(3-2x^4) (chain Rule??)

    thanks for your help
    chain rule

    CB


    ... where



    ... is the product rule



    ... the chain rule. Straight continuous lines differentiate downwards (integrate up) with respect to x, and the straight dashed line similarly but with respect to the dashed balloon expression (the inner function of the composite which is subject to the chain rule).

    Spoiler:

    Spoiler:

    Spoiler:

    _________________________________________

    Don't integrate - balloontegrate!

    Balloon Calculus; standard integrals, derivatives and methods

    Balloon Calculus Drawing with LaTeX and Asymptote!
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