Differentiation Question 363
Question: If $ y=a{x^{n+1}}+b{x^{-n}} $ , then $ x^{2}\frac{d^{2}y}{dx^{2}}= $
[Karnataka CET 1993]
Options:
A) $ n(n-1)y $
B) $ n(n+1)y $
C) ny
D) $ n^{2}y $
Show Answer
Answer:
Correct Answer: B
Solution:
$ y=a{x^{n+1}}+b{x^{-n}}\Rightarrow \frac{dy}{dx}=(n+1)ax^{n}-nb{x^{-n-1}} $
Therefore $ \frac{d^{2}y}{dx^{2}}=n(n+1)a{x^{n-1}}+n(n+1)b{x^{-n-2}} $
Therefore $ x^{2}\frac{d^{2}y}{dx^{2}}=n(n+1)y $ .
BETA
