Given:
[tex]y=\frac{8}{x^4}[/tex]Differentiate y with respect to x,
[tex]\begin{gathered} \frac{dy}{dx}=\frac{d}{dx}(\frac{8}{x^4}) \\ =\frac{d}{dx}(8x^{-4}) \\ \text{Apply rule of derivative,} \\ \frac{d}{dx}(x^n)=nx^{n-1} \\ \frac{dy}{dx}=8(-4)x^{-4-1} \\ \frac{dy}{dx}=-32x^{-5} \\ \frac{dy}{dx}=-\frac{32}{x^5} \end{gathered}[/tex]When x = 2,
[tex]\begin{gathered} \frac{dy}{dx}=-\frac{32}{2^5} \\ =-\frac{32}{32} \\ =-1 \end{gathered}[/tex]Now, eastimate the value of,
[tex]\begin{gathered} y=\frac{8}{x^4}\text{ at x=1.99} \\ y=\frac{8}{(1.99)^4} \\ y=0.510\text{ } \end{gathered}[/tex]Answer:
[tex]\begin{gathered} \frac{dy}{dx}=-\frac{32}{x^5} \\ At\text{ x=2} \\ \frac{dy}{dx}=-1 \end{gathered}[/tex]