NTA Abhyas JEE Main2020MathematicsDifferentiationPractice

If ϕ x = log 8 ⁡ log 3 ⁡ x , then ϕ ′ e is equal to

Options

Ae log ⁡ 8
B– e log ⁡ 8
C1 e log ⁡ 8
DNone of these

Correct answer

C. 1 e log ⁡ 8

Step-by-step solution

We have, ϕ x = log 8 ⁡ log 3 ⁡ x = log 8 ⁡ log ⁡ x log ⁡ 3 = log 8 ⁡ log ⁡ x - log 8 ⁡ log ⁡ 3 = log ⁡ log ⁡ x log ⁡ 8 - log 8 ⁡ log ⁡ 3 ϕ ′ x = 1 log 8 ⋅ 1 log x ⋅ 1 x − 0 ∴ ϕ ′ e = 1 log 8 ⋅ 1 log e ⋅ 1 e = 1 e log 8

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