If I_n=d^ndx^nx^nln⁡x, then the value of 1/50I_7-7I_6 is equal to

Correct answer: 14.4. Ι_n=d^(n-1)dx^(n-1)x^(n-1)+nx^(n-1)ln⁡x ⇒I_n=n-1!+nI_(n-1)⇒I_n-nI_(n-1)=n-1! Putting n=7, we get, I_7-7I_6=6!=720

Q1 / 46 · NTA Abhyas (JEE Main) 2020 · Mathematics · Differentiation

If $I_{n} = \frac{d^{n}}{d x^{n}} (x^{n} \ln x)$ , then the value of $\frac{1}{50} (I_{7} - 7 I_{6})$ is equal to

Correct answer: 14.4

Ι_{n} = \frac{d^{n - 1}}{{dx}^{n - 1}} (x^{n - 1} + {nx}^{n - 1} \ln x)

\Rightarrow I_{n} = (n - 1)! + n I_{n - 1} \Rightarrow I_{n} - n I_{n - 1} = (n - 1)!

Putting

n = 7

, we get,

I_{7} - 7 I_{6} = 6! = 720

Hence, the correct answer is 14.4.