Method of DifferentiationeasyFree

Method of Differentiation: Equals

JEE Maths question with a full step-by-step solution.

Question
If f(x)=log⁡xf(x)=\log x, then f′(log⁡x)f'(\log x) equals
Axlog⁡x\dfrac{x}{\log x}
Blog⁡xx\dfrac{\log x}{x}
C1xlog⁡x\dfrac{1}{x\log x}
D1log⁡x\dfrac{1}{\log x}correct
Solution
Step 1: f(x)=log⁡x  ⇒  f′(x)=1xf(x)=\log x\;\Rightarrow\;f'(x)=\dfrac{1}{x}. Step 2: Substitute x↦log⁡xx\mapsto\log x into f′f':
f′(log⁡x)=1log⁡xf'(\log x)=\dfrac{1}{\log x}
 Correct answer: (4)
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