SOLUTION: Assalma-o-Alaikum sir just tell me that why we take the exponent -1 in Differential Calculus please reply me Sharp. the formula is nx-1 where n-1 is the power of x.

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Question 762179: Assalma-o-Alaikum
sir just tell me that why we take the exponent -1 in Differential Calculus please reply me Sharp. the formula is nx-1 where n-1 is the power of x.



With Regard
Gulzar Ahmad
Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


First you need to accept (or read and understand the proof of) the theorem that says


Difference of Two n th Powers

If a and b are real numbers, and n is a positive integer, then

    an - bn = (a-b)(an-1 + an-2b + an-3b2 + . . . + abn-2 + bn-1).


See Difference of Two Powers if you need to see the proof of the above.

Start with

Then since we can substitute and get:



Apply the Difference of Two n-th Powers Theorem:



Simplify the numerator:



Cancel the



Since we don't have in the denominator any longer, take the limit:



Simplify




Then, since there are terms:



Wa alaykumu s-salam

John

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