(d^n)/(dx^n)(logx)=? (a)((n-1)!)/(x^n) ...

`(d^n)/(dx^n)(logx)=?` (a)`((n-1)!)/(x^n)` (b) `(n !)/(x^n)` (c)`((n-2)!)/(x^n)` (d) `(-1)^(n-1)((n-1)!)/(x^n)`

`((n-1)!)/(x^(n))`

`(n!)/(x^(n))`

`((n-2)!)/(x^(n))`

`(-1)^(n-1)((n-1)!)/(x^(n))`

Text Solution

Verified by Experts

Let y=log x. `"Then,"`
`y_(1)=(1)/(x),y_(2)=(-1)/(x^(2)),y_(3)=(2)/(x^(3)),...,y_(n)=((-1)^(n-1)(n-1)!)/(x^(n)).`

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