Mathematics - Differentiation Question with Solution | TestHub

$$8f(x)+6f\left(\frac{1}{x}\right)=x+5$$

Replacing x by $\frac{1}{x}$, we set

$$6f(x)+8f\left(\frac{1}{x}\right)=\frac{1}{x}+5$$

From (1) \& (2)

$$f(x)=\frac{1}{28}\left(8x-\frac{6}{x}+10\right)$$

$\therefore y=x^{2}f(x)=\frac{1}{28}\left[8x^3-6x+10x^2\right]$

$$\frac{dy}{dx}=\frac{1}{28}\left[24x^2-6+20x\right]$$

$${\left(\frac{dy}{dx}\right)}_{(x=-1)}=\frac{1}{28}(24-6-20)=-\frac{1}{14}$$