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If y = sec(tan⁻¹ x), then dy/dx at x = 1 is equal to

1. 1
2. sqrt(2)
3. 1/sqrt(2)
4. 1/2

Correct answer: 1/sqrt(2)

Solution

To find dy/dx, we first differentiate y = sec(tan⁻¹ x) using the chain rule and implicit differentiation. At x = 1, the calculations yield dy/dx = 1/sqrt(2), confirming that this is the correct answer.

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