If $ 5 f(x)+3 f\left(\frac{1}{x}\right)=x+2 $ and $ y=x f(x) $ then $ \left(\frac{d y}{d x}\right)_{x=1} $ is equal to

Question

If $ 5 f(x)+3 f\left(\frac{1}{x}\right)=x+2 $ and $ y=x f(x) $ then $ \left(\frac{d y}{d x}\right)_{x=1} $ is equal to, $ \frac{1}{4} $, $ \frac{7}{8} $, $ 1 $, None of these

MARKS App · Accepted Answer

5 ƒ x + 3 ƒ 1 x = x + 2 … 1 Replacing x by 1 x ∴ 5 ƒ 1 x + 3 ƒ x = 1 x + 2 … 2 From 1 25 ƒ x + 15 ƒ 1 x = 5 x + 10 … 3 and from 2 9 ƒ x + 15 ƒ 1 x = 3 x + 6 … 4 Subtracting 4 from 3 ∴ 16 ƒ x = 5 x - 3 x + 4 ∴ xƒ x = 5 x 2 - 3 + 4 x 16 = y ∴ d y d x = 10 x + 4 16 d y d x x = 1 = 10 + 4 16 = 7 8 .

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