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Thread: Trouble finding basic derivatives

  1. #1
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    Trouble finding basic derivatives

    I understand the formula to find derivatives, but for some reason I can't seem to get the right answer when applying said formula most of the time. Here's an example, maybe someone could walk me through step by step?

    3x^2-x^3

    Now I used an online derivative calculator and got the answer, but I still can't even come to that answer when I try to apply the lim (h--0) f(x+h)-f(x) over H formula. I keep getting -3x^2+2x and the correct answer is 6x-3x^2
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  2. #2
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    Ill get you started..

    So $\displaystyle f(x) = 3x^2 - x^3$

    Now to compute the derivative we put $\displaystyle f(x)$ into the definition of the derivative.
    that is:
    $\displaystyle \lim_{ h\to 0} \frac{ f(x+h) - f(x)}{h}$ (the definition of a derivative)

    Now.. ($\displaystyle f(x)= 3x^2-x^3$ into the definition)
    $\displaystyle \lim_{ h\to 0} \frac{ 3(x+h)^2-(x+h)^3 - (3x^2 - x^3) }{h}$

    After expanding we get:

    $\displaystyle = \lim_{ h\to 0} \frac{3(x^2+2hx+h^3)-(x^3+3x^2h+3xh^2+h^3) - 3x^2 +x^3}{h}$

    Canceling terms.. and to the end of the problem...

    $\displaystyle = \lim_{ h\to 0} \frac{6hx+3h^2-3x^2h-3xh^2-h^3}{h} $

    $\displaystyle = \lim_{ h\to 0} 6x+3h-3x^2-3xh-h^2 $

    $\displaystyle = 6x-3x^2$
    Last edited by Scopur; Oct 16th 2008 at 03:43 PM.
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