f-x-2f-1-x-3x-f-x-

Question Number 207402 by MATHEMATICSAM last updated on 13/May/24

f (x) + 2 f (\frac{1}{x}) = 3 x .

f^{'} (x) = ?

Answered by Frix last updated on 13/May/24

x = t : f (t) + 2 f (\frac{1}{t}) = 3 t

x = \frac{1}{t} : f (\frac{1}{t}) + 2 f (t) = \frac{3}{t}

\Rightarrow f (t) = \frac{2}{t} - t [\land f (\frac{1}{t}) = 2 t - \frac{1}{t}]

\Rightarrow f^{'} (x) = - \frac{2}{x^{2}} - 1

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