If y = (^-1x) , then dy/dx at x = 1 is equal to: - Mathematics MCQ JEE Main 2026 | ExamTest.live

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If y = sec (tan^{- 1} x), then \frac{d y}{d x} at x = 1 is equal to:

Solution & Step-by-step Explanation

Let θ = tan^{- 1} x \Rightarrow tan θ = x .Then y = sec θ . Since sec^{2} θ = 1 + tan^{2} θ, we have y = 1 + x^{2} .Differentiate w.r.t x : \frac{d y}{d x} = \frac{1}{2 1 + x ^{2}} \cdot 2 x = \frac{x}{1 + x ^{2}} At x = 1 : \frac{d y}{d x} = \frac{1}{1 + 1 ^{2}} = \frac{1}{2}

Try it yourself before checking the explanation above.

If y = sec (tan^{- 1} x), then \frac{d y}{d x} at x = 1 is equal to:

1/2

1

\sqrt{2}

1/\sqrt{2}

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