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PUNE MCA Exam 2016 Question Paper with answers for online practice

Question : 40 of 50

Marks: +1, -0

The derivation of f(lox x), f(x) =log x is;

Solution:

Concept:

Use the chain rule to differentiate the composition

f(\log x)

where

f(x)=\log x

Explanation:

First, write the composition:

f(\log x) = \log(\log x)

Differentiate using the chain rule:

\frac{d}{dx} \log(\log x) = \frac{1}{\log x} \cdot \frac{d}{dx}(\log x)

The derivative of

\log x

\frac{1}{x}

So the result is

\frac{1}{\log x} \cdot \frac{1}{x} = \frac{1}{x \log x}

Answer:

\frac{1}{x \log x}

, which corresponds to option B.

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