Explanation

(b)
$5f(x) + 3f\left( \frac{1}{x} \right) = x + 2\ \ldots(i)$
On replacing $x$ by $\frac{1}{x}$, we get
$5f\left( \frac{1}{x} \right) + 3f(x) = \frac{1}{x} + 2\ \ldots(ii)$
On multiplying Eq. (i) by 5 and Eq. (ii) by 3 and then on subtracting, we get
$\therefore 16f(x) = 5x - \frac{3}{x} + 4$
$\Rightarrow xf(x) = \frac{5x^{2} - 3 + 4x}{16} = y$
$\therefore\frac{dy}{dx} = \frac{10x + 4}{16}$
$\left. \ \frac{dy}{dx} \right|_{x = 1} = \frac{10 + 4}{16} = \frac{7}{8}$