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find the n th derivative of ( x n-1 logx ) using leibnitz theorem

find the nth derivative of ( xn-1 logx ) using leibnitz theorem

Grade:12th pass

1 Answers

Vikas TU
14149 Points
3 years ago
Dear Student,
 
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  •  
F1n-1  = xn-2 + (n-1)xn-2logx
=  xn-2 + (n-1)Fn-2
differentiate again to get:
F2n-1 = (n-2)xn-3  + (n-1) xn-3 +(n-1)(n-2)Fn-3
similarly we can say that,
Fnn-1 = (n-1)(n-2)(n-3) ........3.2.1 xn-n
          =(n-1)!                          [Ans]
Cheers!!
Regards,
Vikas (B. Tech. 4th year
Thapar University)

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