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JEE Main201912 Apr 2019Evening ShiftMathematicsDifferentiationActual

The derivative of t a n - 1 s i n x - c o s x s i n x + c o s x with respect to x 2 , where x ∈ 0 , π 2 , is

Options

  1. A2
  2. B1 2
  3. C2 3
  4. D1

Correct answer

A. 2

Step-by-step solution

Given function can be written as y = tan - 1 sin x - cos x sin x + cos x ⇒   y = tan - 1 tan x - 1 tan x + 1 ⇒   y = tan - 1 tan x - π 4   given   x ∈ 0 , π 2 ⇒   y = x - π 4 Now d y d x 2 = 2 d y d x = 2

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