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Math Help - Derivative Functions

  1. #1
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    Derivative Functions

    I need to find the derivative of this function algebraically: y = (x – 1)^3 + 2



    Please help!



    Thank-you in advance,
    K-L
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  2. #2
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    Do you mean by using the definition?

    Can you do this one y = x^{2}?

    How about this one y = x^{2} + 32?
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  3. #3
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    The question says:

    Consider the graph of y= (x-1)^3 +2
    Use your rules of differentiation to find the derivative y' algebraically.

    I don't really understand it.
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  4. #4
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    First, letís write it as y(x) = \left( {x - 1} \right)^3  + 2.
    Then we have, \begin{array}{rcl}<br />
 \frac{{dy}}{{dx}} & = & \lim _{h \to 0} \frac{{y(x + h) - y(x)}}{h} \\ <br />
  & = & \lim _{h \to 0} \frac{{\left[ {\left( {x + h - 1} \right)^3  + 2} \right] - \left[ {\left( {x - 1} \right)^3  + 2} \right]}}{h} \\ <br />
 \end{array}
    Now you do the algebra.
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  5. #5
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    Thanks, that's already helped quite a bit.
    Though I think I'm doing something wrong when I expand it:

    (x^3 + h^3 + 3xh + 3xh -1^3 +2) - (x^3 -1^3 +2)
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  6. #6
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    You need a great deal of practice on simple algebra.
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