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Math Help - Higher Derivatives

  1. #1
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    Higher Derivatives

    How do I find the first and second derivatives of the function:
    y = x^{n}?
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  2. #2
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    Power Rule

    While it looks more confusing than most, remember that "n" in the exponent is just a number (I assume) - it's not a variable like x.

    Thus, just use the power rule.

    Imagine it was, say, y = x^4. The power rule says, basically, bring down the power and, for the new power, subtract 1 from the original. This gives y' = 4x^3.

    Use the same thought process for y = x^n. Bring the power down, so now you are multiplying by n, and reduce the original power by 1, so your new power is (n-1).

    Thus, the first derivative is y' = nx^(n-1).

    Repeat this process to find the second derivative - bring the power down and reduce it by one for the new power.

    Hope this helps - sorry it's not in nice type - I haven't had a chance to re-learn that stuff.
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