Question

Find the derivative of tan⁻¹(x) + cos⁻¹(x)

• A. $\frac11+x^2$
• B. 0
• C. $\frac-11+x^2$
• D. None of these

Hint:

Remember the sum identity: tan⁻¹(x) + cos⁻¹(x) = π/2 for all real x, which simplifies the derivative calculation.

Answer 1

The Correct Option is A

Step 1: Apply derivative rules.
The derivative of tan⁻¹(x) is 1 / (1 + x²), and the derivative of cos⁻¹(x) is -1 / √(1 - x²). 
Since tan⁻¹(x) + cos⁻¹(x) = π/2 for all real x, the derivative of the sum is 0.

 Step 2: Conclusion.
The derivative of tan⁻¹(x) + cos⁻¹(x) is 0.

 Final Answer: 0