The derivative of cos⁻¹(1 − x²)/(1 + x²) with respect to tan⁻¹ x is:
The derivative of cos⁻¹(1 − x²)/(1 + x²) with respect to tan⁻¹ x is:
- A. 2
- B. −2
- C. 1
- D. −1
Answer: A) 2
Explanation: Let u = cos⁻¹((1−x²)/(1+x²)) = 2 tan⁻¹ x for x≥0. v = tan⁻¹ x. du/dx = 2/(1+x²), dv/dx = 1/(1+x²). du/dv = 2.
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