Differentiate sec⁻¹(1 / (2x² − 1)) with respect to x, where 0 < x < 1/√2.
Differentiate sec⁻¹(1 / (2x² − 1)) with respect to x, where 0 < x < 1/√2.
- A. 2 / √(1 − x²)
- B. −2 / √(1 − x²)
- C. 1 / √(1 − x²)
- D. −1 / √(1 − x²)
Answer: B) −2 / √(1 − x²)
Explanation: Let x = cos θ. 2x² − 1 = 2cos²θ − 1 = cos 2θ. sec⁻¹(1/cos 2θ) = sec⁻¹(sec 2θ) = 2θ = 2 cos⁻¹x. Derivative is −2 / √(1 − x²).
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