Derivative of y = x^n - Part 2: General Power Rule

in #mathematics2 months ago (edited)

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 Resized AI.jpg

General Power Rule: n is any real number


Example 1

Derivative of y = x1.3



Example 2

Derivative of y = xx1/2





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