Question

If \[ y=\left(x+\sqrt{x^{2}+1}\right)^{5}, \] then \(25y=\)

• A. \((x^{2}+1)y_{2}-xy_{1}\)
• B. \((x^{2}+1)y_{2}+xy_{1}\)
• C. \((x^{2}+1)y_{2}-2xy_{1}\)
• D. \((x^{2}+1)y_{2}+2xy_{1}\)

Hint:

Remember the standard identity \[ \boxed{ \frac{d}{dx} \ln\!\left(x+\sqrt{x^{2}+1}\right) = \frac1{\sqrt{x^{2}+1}}. } \] It greatly simplifies repeated differentiation problems involving \[ x+\sqrt{x^{2}+1}. \]

Answer 1

The Correct Option is B