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ECAT Mathematics QUESTION #772
Question 1
If \(y = \sqrt{a^2 + x^2}\), then \(\dfrac{dy}{dx} = ?\)
  • \(\dfrac{x}{\sqrt{a^2 + x^2}}\)✔️
  • \(\dfrac{\sqrt{a^2 + x^2}}{x}\)
  • \(x\sqrt{a^2 - x^2}\)
  • None
Correct Answer Explanation
Using chain rule: \(\dfrac{dy}{dx} = \dfrac{1}{2\sqrt{a^2+x^2}} \cdot 2x = \dfrac{x}{\sqrt{a^2+x^2}}\).