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AP EAMCET202120 Aug 2021Evening ShiftMathematicsDifferentiationActual

If y = ( log cot x tan x ) ( log tan x cot x ) + tan - 1 4 x 4 - x 2 , then d y d x =

Options

  1. A1 4 + x 2
  2. B4 4 + x 2
  3. C1 4 - x 2
  4. D4 4 - x 2

Correct answer

B. 4 4 + x 2

Step-by-step solution

y = ( log cot x tan x ) ( log tan x cot x ) + tan - 1 4 x 4 - x 2 y = log tan x log c o t x log c o t x log tan x + tan - 1 4 x 4 - x 2 y = 1 + tan - 1 4 x 4 - x 2 y ' = 0 + d d x tan - 1 4 x 4 - x 2 = 1 1 + 4 x 4 - x 2 2 d d x 4 x 4 - x 2 = 1 1 + 16 x 2 16 - 8 x 2 + x 4 4 - x 2 4 - 4 x - 2 x 4 - x 2 2 = 4 4 + x 2

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