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pritam samanta Grade: 12
        how to find n-th  derivative of a function f(x)=[x^(n-1)]logx what will be n-th  derivate of f(x)
7 years ago

Answers : (3)

Badiuddin askIITians.ismu Expert
147 Points
										

Dear pritam


Fn-1(x)=x(n-1)logx


differentiate


F1n-1  = xn-2 + (n-1)xn-2logx


          =  xn-2 + (n-1)Fn-2


again differentiate


F2n-1 = (n-2)xn-3  + (n-1) xn-3 +(n-1)(n-2)Fn-3


similerly


Fnn-1 = (n-1)(n-2)(n-3) ........3.2.1 xn-n


           =(n-1)!


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Badiuddin



7 years ago
Amrita
8 Points
										this answer is wrong. The correct answer is (n-1)!/x
You can get the answer by successively differentiating and finally reaching a step where
(n-1)(n-2)....(n-(n-1))D^(n-(n-1){(x^(n-n)*logx} = (n-1)! d/dx(logx) = (n-1)!/x
3 years ago
yeshwanth
19 Points
										
D^n (x^n logx)
2 years ago
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