In this video I derive the General Power Rule for any real number n, and it happens to be the same as the one I derived for positive integers. I use the method of Logarithmic Differentiation in deriving it because it simplifies the differentiation by bringing the exponent down to a simpler expression.

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Derivative of y = xn

General Power Rule: n is any real number

Example 1

Derivative of y = x^1.3

Solution:

Example 2

Derivative of y = x^x1/2

Solution: