If I n = d n d x n x n ln ⁡ x , then the value of 1 50 I 7 - 7 I 6 is equal to

Question

If I n = d n d x n x n ln ⁡ x , then the value of 1 50 I 7 - 7 I 6 is equal to,

MARKS App · Accepted Answer

Ι n = d n - 1 dx n - 1 x n - 1 + nx n - 1 ln ⁡ x ⇒ I n = n - 1 ! + n I n - 1 ⇒ I n - n I n - 1 = n - 1 ! Putting n = 7 , we get, I 7 - 7 I 6 = 6 ! = 72 0

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