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3 Differentiation Rules

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  • 02-06-2008 7:41pm
    #1
    Decerto
    Registered Users Posts: 309 ✭✭


    The proofs for the 3 rules, sum, product and quotient, do they have to be done using f(x+h)-f(x) or can you use the log way


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    #2
    mike-gunners
    Closed Accounts Posts: 33 ✭mike-gunners


    unless you are asked to prove them from 1st pronciples, you can prove them via log method(which is simple).I'd make sure i know my Perpendicular Distance Proof.as well as De moivre


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    #3
    eoin2nc
    Registered Users Posts: 688 ✭✭✭eoin2nc


    What is the log method? I only know how to do it using 1st principles


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    #4
    Cokehead Mother
    Closed Accounts Posts: 773 ✭✭✭Cokehead Mother


    eoin2nc wrote: »
    What is the log method? I only know how to do it using 1st principles

    You won't be able to use it in the exam because they always ask for first principles but say for example the product rule:

    y = uv
    lny = ln(uv)
    lny = lnu + lnv

    Then you differentiate both sides and get

    1/y (dy/dx) = 1/u (du/dx) + 1/v (dv/dx) [chain rule]

    so dy/dx = y [1/u (du/dx) + 1/v (dv/dx)]

    And then you change y back to uv, and it becomes

    dy/dx = v(du/dx) + u(dv/dx)


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