How do I find the first and second derivatives of the function:

$\displaystyle y = x^{n}$?

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- Feb 26th 2008, 02:49 PM!!!Higher Derivatives
How do I find the first and second derivatives of the function:

$\displaystyle y = x^{n}$? - Feb 26th 2008, 03:17 PMMathnasiumPower 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.