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Thread: finding derivatives from first principles

  1. #1
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    finding derivatives from first principles

    Hi I'm still struggling with finding the definition of the derivative (from first principles),

    find f'(x) of f(x)=-2x^2+4x-7
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  2. #2
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    Re: finding derivatives from first principles

    Quote Originally Posted by calmo11 View Post
    Hi I'm still struggling with finding the definition of the derivative (from first principles),

    find f'(x) of f(x)=-2x^2+4x-7
    Given $f(x), f'(x) = \displaystyle{\lim_{h\to 0}}\dfrac{f(x+h)-f(x)}{h}$


    $f(x)=-2x^2+4 x - 7$

    $f'(x)=\displaystyle{\lim_{h \to 0}}\dfrac{\left(-2(x+h)^2+4(x+h)-7\right)-\left(-2x^2+4x-7\right)}{h}$

    $f'(x)=\displaystyle{\lim_{h \to 0}}\dfrac{-4hx +4h-2h^2}{h}$

    $f'(x)=\displaystyle{\lim_{h \to 0}}~-4x+4-2h=-4x+4$
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