CUET · MATHS · PYQ PAPER 2025
If \(y=\left(x+\sqrt{x^2+1}\right)^m\), then \(\frac{d y}{d x}\) is
- A \(\frac{y}{\sqrt{x^2+1}}\)
- B \(\frac{m^2 y}{\sqrt{x^2+1}}\)
- C \(\frac{m}{\sqrt{x^2+1}}\)
- D \(\frac{m y}{\sqrt{x^2+1}}\)
Answer & Solution
Correct Answer
(C) \(\frac{m}{\sqrt{x^2+1}}\)
Step-by-step Solution
Detailed explanation
\(\frac{d y}{d x} = m\left(x+\sqrt{x^2+1}\right)^{m-1} \cdot \frac{d}{d x}\left(x+\sqrt{x^2+1}\right)\) \(\frac{d y}{d x} = m\left(x+\sqrt{x^2+1}\right)^{m-1} \cdot \left(1 + \frac{1}{2\sqrt{x^2+1}} \cdot 2x\right)\)…
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