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

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Application +4 | -1

5f\left( x \right) + 3f\left( {\frac{1}{x}} \right) = x + 2

and

y = x\mathrm{ }f\left( x \right),

then

{\left( {\frac{{dy}}{{dx}}} \right)_{x = 1}}

is equal to

View answer and explanation

Correct option: B

\frac{7}{8}

Option B (

\frac{7}{8}

) is correct because solving the system of equations and differentiating yields the correct result at x=1.

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