Find the derivative of tan⁻¹(2x / (1 − x²)) with respect to x.
Find the derivative of tan⁻¹(2x / (1 − x²)) with respect to x.
- A. 1 / (1 + x²)
- B. 2 / (1 + x²)
- C. −2 / (1 + x²)
- D. 2x / (1 + x²)
Answer: B) 2 / (1 + x²)
Explanation: Using inverse trigonometric substitution, let x = tan θ. The expression becomes tan⁻¹(tan 2θ) = 2θ = 2 tan⁻¹x. Its derivative is 2 / (1 + x²).
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