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AP EAMCET202023 Sep 2020Morning ShiftMathematicsDifferentiationActual

If y = tan - 1 4 x 1 + 5 x 2 + tan - 1 2 + 3 x 3 - 2 x , then d y d x =

Options

  1. A1 1 + 25 x 2 + 2 1 + x 2
  2. B5 1 + 25 x 2 + 2 1 + x 2
  3. C5 1 + 25 x 2
  4. D1 1 + 25 x 2

Correct answer

C. 5 1 + 25 x 2

Step-by-step solution

y = tan - 1 4 x 1 + 5 x 2 + 2 + 3 x 3 - 2 x 1 - 4 x 1 + 5 x 2 2 + 3 x 3 - 2 x y = tan - 1 12 x - 8 x 2 + 2 + 10 x 2 + 3 x + 15 x 3 3 + 15 x 2 - 2 x - 10 x 3 - 8 x - 12 x 2 = tan - 1 15 x 3 + 2 x 2 + 15 x + 2 - 10 x 3 + 3 x 2 - 10 x + 3 y = tan - 1 15 x + 2 ( x 2 + 1 ) ( 3 - 10 x ) ( x 2 + 1 ) = tan - 1 15 x + 2 3 - 10 x d y d x = 1 1 + 15 x + 2 3 - 10 x 2 × 15 ( 3 - 10 x ) + 10 ( 15 x + 2 ) ( 3 - 10 x ) 2 = 1 9 + 100 x 2 - 60 x + 225 x 2 + 60 x + 4 × 65 1 = 65 325 x 2 + 13 = 5 25 x 2 + 1

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