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NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If y = log 10 ⁡ x + log x ⁡ 10 + log x ⁡ x + log 10 ⁡ 10 , then d y d x is equal to

Options

  1. A1 x log e ⁡ 10 - log e ⁡ 10 x log e ⁡ x 2
  2. B1 x log e ⁡ 10 - 1 x log 10 ⁡ e
  3. C1 x log e ⁡ 10 - log e ⁡ 10 x log e ⁡ x
  4. DNone of these

Correct answer

A. 1 x log e ⁡ 10 - log e ⁡ 10 x log e ⁡ x 2

Step-by-step solution

y = log 10 ⁡ x + log x ⁡ 10 + log x ⁡ x + log 10 ⁡ 10 = log 10 ⁡ x + log e ⁡ 10 log e x + 1 + 1 ⇒ d y d x = 1 x log 10 ⁡ e - log e ⁡ 10 x log e ⁡ x 2

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