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how to find n-th derivative of a function f(x)=[x^(n-1)]logx what will be n-th derivate of f(x)

how to find n-th derivative of a function f(x)=[x^(n-1)]logx what will be n-th derivate of f(x)

Grade:12

3 Answers

Badiuddin askIITians.ismu Expert
148 Points
12 years ago

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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Amrita
8 Points
8 years ago
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
yeshwanth
19 Points
7 years ago
D^n (x^n logx)

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