JEE Main2013MathematicsDifferentiationActual

If y = sec tan - 1 x , then d y d x at x = 1 is equal to

Options

A1
B2
C1 2
D1 2

Correct answer

C. 1 2

Step-by-step solution

Given, y = sec tan - 1 x Differentiating both sides w.r.t. x , we get, d y d x = sec tan - 1 x tan tan - 1 x · 1 1 + x 2 At x = 1 , we have, tan - 1 x = π 4 d y d x = sec π 4 × tan π 4 1 + 1 2 = 2 2 = 1 2

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