JEE MATHEMATICS MCQ: DIFFERENTIATION

1 Easy

1 of 1

Analyzing +4 | -1

f\left( x \right) = \frac{{x - 1}}{4} + \frac{{{{\left( {x - 1} \right)}^3}}}{{12}} + \frac{{{{\left( {x - 1} \right)}^5}}}{{20}} + \frac{{{{\left( {x - 1} \right)}^7}}}{{28}} + \ldots ,

where

0 < x < 2

, then

f'\left( x \right)

is equal to

View answer and explanation

Correct option: A

\frac{1}{{4x\left( {2 - x} \right)}}

Option A (

\frac{1}{{4x\left( {2 - x} \right)}}

) is the correct derivative, obtained by recognizing the series as a logarithmic form and then differentiating.

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