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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Mathematics
Chapter
Differentiation

NTA Abhyas 2020 · Mathematics · Differentiation

If I _ n = d ^ n d x ^ n ( x ^ n ln x) , then the value of...

If In=dndxn(xnlnx){I}_{n} = \dfrac{{d}^{n}}{d{x}^{n}}\left({x}^{n}ln x\right), then the value of 150(I7−7I6)\dfrac{1}{50}\left({I}_{7} - 7{I}_{6}\right) is equal to

Correct answer

14.4

Step-by-step solution

In=dn−1dxn−1(xn−1+nxn−1lnx){Ι}_{n} = \dfrac{{d}^{n - 1}}{{dx}^{n - 1}}\left({x}^{n - 1} + {nx}^{n - 1}ln x\right)
⇒In=(n−1)!+nIn−1⇒In−nIn−1=(n−1)!⇒ {I}_{n} = \left(n - 1\right) ! + n{I}_{n - 1} ⇒ {I}_{n} - n{I}_{n - 1} = \left(n - 1\right) !
Putting n=7n = 7, we get,
I7−7I6=6!=720{I}_{7} - 7{I}_{6} = 6 ! = 720
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