Given the function f(x), we can write it like this:
[tex]\begin{gathered} f(x)=-\frac{3}{x^4} \\ \Rightarrow f(x)=-3x^{-4} \end{gathered}[/tex]Using the formula for polynomial derivatives, we get:
[tex]\begin{gathered} f(x)=-3x^{-4} \\ \Rightarrow f^{\prime}(x)=-3\cdot(-4)x^{-4-1}=12x^{-5} \\ f(x)=\frac{12}{x^5} \end{gathered}[/tex]Therefore, the derivative f'(x) is 12/x^5
