CUET PG 2026 — Mathematics PYQ

Solution

To solve this, we apply the standard formulas for the derivatives of inverse trigonometric functions:

1. For A: The derivative of ${\cos }^{-1}x$ is:

   $$\frac{d}{dx}{\cos }^{-1}x=\frac{-1}{\sqrt{1-x^2}}$$

   This matches with III.

2. For B: The derivative of ${\cot }^{-1}x$ is:

   $$\frac{d}{dx}{\cot }^{-1}x=-\frac{1}{1+x^2}$$

   This matches with I.

3. For C: The derivative of ${\text{cosec}}^{-1}x$ is:

   $$\frac{d}{dx}{\text{cosec}}^{-1}x=\frac{-1}{|x|\sqrt{x^2-1}}$$

   This matches with IV.

4. For D: The derivative of ${\sec }^{-1}x$ is:

   $$\frac{d}{dx}{\sec }^{-1}x=\frac{1}{|x|\sqrt{x^2-1}}$$

   This matches with II.

Final Matching:

(A) $\to$ III

(B) $\to$ I

(C) $\to$ IV

(D) $\to$ II

The correct option is (d).