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Math Help - find derivative without using product//chain/or quotient rule..

  1. #1
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    find derivative without using product//chain/or quotient rule..

    Hello,

    Please could someone run through deriving these 2 equations through algebraic expansion.

    d/dx {sqrt(2y)}


    and

    d/dx {-1/((2x)^3)}

    Thankyou in advance.
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  2. #2
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    Re: find derivative without using product//chain/or quotient rule..

    edit ... just figured out the second one..
    the first one I still can't get my head around!

    i'll run through what i'm doing ..

    so,

    d/dx[2y]^1/2

    = 1/2*[2y]^-1/2

    = 1/2*(1/sqrt(2y)

    =1/(2*sqrt(2y)) ....

    i should be getting 1/sqrt(2y) ... where am i going wrong?
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  3. #3
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    Re: find derivative without using product//chain/or quotient rule..

    Sqrt(2x)= sqrt(2)*sqrt(x)
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  4. #4
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    Re: find derivative without using product//chain/or quotient rule..

    Hello, euphmorning!

    the first one . . .

    So: . \frac{d}{dx}\left[(2x)^{\frac{1}{2}}\right]

    . . . . =\;\tfrac{1}{2}\cdot(2x)^{-\frac{1}{2}}{\color{red}\cdot 2}
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  5. #5
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    Re: find derivative without using product//chain/or quotient rule..

    Heya, thanks for the responses.. i'm afraid I still can't see how to arrive @ 1/sqrt(2y)

    :/
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  6. #6
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    Re: find derivative without using product//chain/or quotient rule..

    The sqrt(2) is a constant so take the derivative of sqrt(x). 1/2(sqrt(x)). Multiply by the constant and arrive at sqrt(2)/2(sqrt(x)). Multiply that by sqrt(2)/sqrt(2) to get your answer.
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  7. #7
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    Re: find derivative without using product//chain/or quotient rule..

    Got it at last, thankyou very much.
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