What is a Derivative? Deriving the Power Rule

After discussing differentiation at great length, it is time to connect this concept with the act of taking the derivative of a function. In actuality these mean the same thing, but using the power rule to take the derivative of a function is actually much simpler than all that business with limits and tangent lines! But it is important to know what the power rule is and where it comes from, so let’s derive it together. This way, when you take the derivatives of functions, you’ll know exactly what is really happening.

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