This topic contains 5 replies, has 4 voices, and was last updated by 2plus2 3 years, 11 months ago.
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Tagged: calculus, derivative, nth
This topic contains 5 replies, has 4 voices, and was last updated by 2plus2 3 years, 11 months ago.
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February 23, 2012 at 5:14 pm #432  
pin690 Member

What is the nth derivative of nx^n? 
February 23, 2012 at 8:06 pm #438  
thecalculuskid Member

The first derivative is (n)(n)x^(n1)=(n^2)x^(n1). The second derivative is (n^2)(n1)x^(n2). The third derivative is (n^2)(n1)(n2)x^(n3). Interestingly, the nth derivative would be (n^2)(n1)(n2)(n3)….[n(n2)][n(n1)]x^(nn) where x^(nn) is x^0, which is equal to 1, so that term kind of “diappears”…. The other factors can be looked upon in the reverse order and you would get: (1)(2)(3)….(n3)(n2)(n1)n^2 n^2 can be broken down into (n)(n). Hence the nth derivative is n! times n or ….. nn! 
February 23, 2012 at 8:12 pm #442  
practicaldave Member

Good answer @thecalculuskid 
February 23, 2012 at 8:14 pm #443  
thecalculuskid Member

Thanks practicaldave. 
February 23, 2012 at 8:15 pm #444  
thecalculuskid Member

So, what do you think pin? Do I get the point? 😉 
February 23, 2012 at 8:17 pm #445  
2plus2 Member

Yes, great answer. 
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