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Justifying the power rule

​Proving the power rule for derivatives (only the more simple cases).
The power rule tells us how to find the derivative of any expression in the form xn:
The AP Calculus course doesn't require knowing the proof of this rule, but we believe that as long as a proof is accessible, there's always something to learn from it. In general, it's always good to require some kind of proof or justification for the theorems you learn.

Let's first see whether the rule makes sense for y=x and y=x2.

Khan Academy video wrapper
Justifying the power ruleSee video transcript

Now let's prove the rule for positive integer values of n.

Khan Academy video wrapper
Proof of power rule for positive integer powersSee video transcript

We can also prove the rule for y=x.

Khan Academy video wrapper
Proof of power rule for square root functionSee video transcript

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