If f ( t ) = 1 + t 1 − t , then f ′ ( 1/ t ) is equal to

f ′ ( t ) = d t d [ 1 + t 1 − t ] = ( 1 + t ) 2 ( 1 + t ) ( − 1 ) − ( 1 − t ) × ( 1 ) = ( 1 + t ) 2 − 1 − t − 1 + t = ( 1 + t ) 2 − 2 f ′ [ 1/ t ] = ( 1 + t 1 ) 2 − 2 = ( t + 1 ) 2 − 2 t 2

Mathematics - Mathematical Reasoning Question with Solution | TestHub

MathematicsMathematical ReasoningGeneralMedium2 minPYQ_2009

MathematicsMediumsingle choice

If $f (t) = \frac{1 - t}{1 + t}$ , then $f^{'} (1/ t)$ is equal to

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Answer:

Solution:

$f^{'} (t) = \frac{d}{d t} [\frac{1 - t}{1 + t}] = \frac{( 1 + t ) ( - 1 ) - ( 1 - t ) \times ( 1 )}{( 1 + t ) ^{2}} = \frac{- 1 - t - 1 + t}{( 1 + t ) ^{2}} = \frac{- 2}{( 1 + t ) ^{2}}$ $f^{'} [1/ t] = \frac{- 2}{( 1 + \frac{1}{t} ) ^{2}} = \frac{- 2 t ^{2}}{( t + 1 ) ^{2}}$

Stream:BITSATSubject:MathematicsTopic:Mathematical ReasoningSubtopic:General

⏱ 2mℹ️ Source: PYQ_2009

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