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Math Help - Derivate and differential equation

  1. #1
    Junior Member
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    Derivate and differential equation (Mod: move to calculus)

    Hello

    1 Derivate the function \frac{3}{\sqrt{x - 9} }

    2 General solution for y' - 3y = e^{-2x} + 2

    --------------------------

    1 I think I have solved this:

    First, lets see the expression as two factors:

    3 * (x - 9)^{-\frac{1}{2}}

    Derivate of an product u' * v + u * v'

    Gives us:

    3* -\frac{1}{2}(x - 9)^{-\frac{3}{2}} + 0 * (x - 9)^{-\frac{1}{2}}

    \frac{3}{2(x - 9)^{\frac{3}{2}}}

    2, I don't know, we haven't really studied differential equations that much.

    Thanks for all replies
    Last edited by λιεҗąиđŗ; May 13th 2008 at 08:25 PM.
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  2. #2
    Super Member angel.white's Avatar
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    With constants, you don't need to use the product rule (it gives the correct answer still, though).

    But, you forgot to transcribe your negative sign.

    meaning:
    f(x) = 3 (x-9)^{-1/2}

    f\prime (x) = 3*\frac{-1}{2}(x-9)^{-3/2}*1

    f\prime (x) = -\frac{3}{2}(x-9)^{-3/2}

    no need for product rule, just chain rule, and since x-9 differentiates to 1, it doesn't even really matter if you use the chain rule on this one.
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