GATE AG 2017 • Q28 MCQ • 1 Mark

Section 1: Engineering Mathematics

Calculus

Subtopic: Limit, continuity and differentiability

Question Statement:

Differentiation of $\sqrt{1+x^2}$ gives

Options:

  • (A) $\frac{1}{1+x^2}$
  • (B) $\frac{1}{\sqrt{1+x^2}}$
  • (C) $\frac{\sqrt{1+x^2}}{x}$
  • (D) $\frac{x}{\sqrt{1+x^2}}$

Official Answer Key:

D

Step-by-Step Solution & Explanation

• Let y = (1+x²)^(1/2). By the chain rule, dy/dx = (1/2)(1+x²)^(–1/2)·(2x) = x/√(1+x²). • Distractor logic: (A) and (B) drop the numerator x that the chain rule introduces; (C) inverts the result. • Final Answer: (D) x/√(1+x²)

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