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NDA 2023 Maths · Mathematics · Derivatives · hard

If y=ln (x+√(1+x^2), then dy/dx is equal to

Single correct option

If y=ln⁡(x+1+x2)y=\ln\left(x+\sqrt{1+x^2}\right), then dydx\dfrac{dy}{dx} is equal to
  1. A. x1+x2\dfrac{x}{\sqrt{1+x^2}}
  2. B. 1+x2\sqrt{1+x^2}
  3. C. 11+x2\dfrac1{\sqrt{1+x^2}}
  4. D. 1x+1+x2\dfrac1{x+\sqrt{1+x^2}}
Show answer and solution

Answer: (C) 11+x2\dfrac1{\sqrt{1+x^2}}

y′=1+x1+x2x+1+x2=(1+x2+x)/1+x2x+1+x2=11+x2y'=\dfrac{1+\frac{x}{\sqrt{1+x^2}}}{x+\sqrt{1+x^2}}=\dfrac{(\sqrt{1+x^2}+x)/\sqrt{1+x^2}}{x+\sqrt{1+x^2}}=\dfrac1{\sqrt{1+x^2}}. The option 1x+1+x2\dfrac1{x+\sqrt{1+x^2}} forgets to differentiate the inside of the logarithm.
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Original question written in the NDA 2023 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake