What is the derivative of cot⁻¹((1 + x) / (1 − x)) with respect to x?
What is the derivative of cot⁻¹((1 + x) / (1 − x)) with respect to x?
- A. 1 / (1 + x²)
- B. −1 / (1 + x²)
- C. 2 / (1 + x²)
- D. −2 / (1 + x²)
Answer: B) −1 / (1 + x²)
Explanation: Let x = tan θ. (1 + tan θ)/(1 − tan θ) = tan(π/4 + θ). cot⁻¹(tan(π/4 + θ)) = cot⁻¹(cot(π/2 − (π/4 + θ))) = π/4 − θ = π/4 − tan⁻¹x. Derivative is −1 / (1 + x²).
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