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Math Help - Differentiate from first principles?

  1. #1
    Newbie scott_237's Avatar
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    Differentiate from first principles?

    Q1) Given that f(x) = 2x^3 + x , find ;
    (a) the derivative of f(x) with respect to x, from first principles

    can somebody explain the answers that are given here (pdf file) and it is question 1 on the exam paper, and also what exactly is the difference between first principles and regular differentiation? Thanks A LOT!
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hello
    Quote Originally Posted by scott_237 View Post
    Q1) Given that f(x) = 2x^3 + x , find ;
    (a) the derivative of f(x) with respect to x, from first principles

    can somebody explain the answers that are given here
    What is not clear in this answer?

    What exactly is the difference between first principles and regular differentiation?
    Finding f' from first principles means using the definition of the derivative : f'(x)=\lim_{h\to0}\tfrac{f(x+h)-f(x)}{h}. If you had been allowed to use "regular differentiation" you could have used results which are derived from the definition of the derivative. (for example (x^n)'=nx^{n-1})
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