Okay this is Benofschool and going for another attempt to explain the Power Rule...

The following image shows the equation work that was used to derive the rule. I will explain each line after the image.

Line 1: Okay lets find the derivative of x to the power of n at x

Line 2: So we just throw it into the derivative formula like usual

Line 3: We have to expand the binomial in the brackets. There are 3 things to realize. First the first term will be x to the power of n regardless to what n is. Secondly, the next term will always have n as the coefficient and n-1 as the exponent and also multiplied by one h. Finally, every other term will have a unknown coefficient (this coefficient will become irrelevant and you will see later) and the exponent of h will increase by 1. So in the third term the power of h will be 2 and in the fourth it is 3 and so on

Line 4: Now we can get rid of x to the power of n because it is subtracted to zero by the other term.

Line 5: Now we factor out an h. Notice that the first term in Line 4 no long has an h variable in the term and every other term afterward still has an h variable remaining. This is the key to seeing the rule

Line 6: Now the h reduces and you are left with what was in the brackets in Line 5.

Line 7: Now we apply the limit and substitute all the h values with zero since there is no h in the brackets anymore. This will cause all terms containing the h variable to become zero. Since the first term does not contain an h variable, it won't be affected by the limit.

Line 8: This leaves us with the rule because all of the other terms are turned into zero thus not affecting the first term at all.

I hope this helped. If there is any more help required, please talk to Dr. Eviatar or myself for help...

Okay well I tried =P

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## 2 comments:

I'm still confused, sorry. =(

Let's talk about it some more! Thanks, Benchman!

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