NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

The differential coefficient of log 10 ⁡ x with respect to log x 10 is

Options

A1
B- log 10 ⁡ x 2
Clog x 10 2
Dx 2 100

Correct answer

B. - log 10 ⁡ x 2

Step-by-step solution

Let, u = log 10 ⁡ x and v = log x ⁡ 10 ⇒ u = log e ⁡ x log e ⁡ 1 0 and v = log e ⁡ 1 0 log e ⁡ x Now, d u d x = 1 x log e ⁡ 1 0 and d v d x = log e ⁡ 10 - 1 x log e ⁡ x 2 ∴ d u d v = d u / d x d v / d x = 1 x log e ⁡ 10 ÷ - log e ⁡ 1 0 x log e ⁡ x 2 = - log e ⁡ x 2 log e ⁡ 10 2 = - log e ⁡ x log e ⁡ 10 2 = - log 10 ⁡ x 2

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