1 The Power Rule

1 The Power Rule - Next: The Product Rule Up: Derivatives:...

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Next: The Product Rule Up: Derivatives: How to Find Previous: The Basic Rules of The Power Rule Here is one of the most basic rules of calculus, perhaps the single rule that more people think of when someone says, ``What do you remember from calculus?" Besides, it has that great name, The Power Rule. It says: Now what does that mean? Well, n can be any number. So if we let n be 3, we have: If we let n be 5, we have: If we let n be 1, we have: This is worth remembering separately, so let's repeat it so it sticks:
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We could also let n be a negative number. For instance, if n =-2, we have Notice that we can now take the derivative of 1/ x : In fact, n can even be a fraction. So for instance, we can take the derivative of , since: The fact that n needn't be a whole number usually doesn't get mentioned in this part of a course on calculus, but we'll clue you in a little early. That little n could even be a number like or . Then: We know it's tempting to try to simplify the exponent
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1 The Power Rule - Next: The Product Rule Up: Derivatives:...

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