ANSWER
[tex]\text{f(x) = -}\frac{5}{x^2}[/tex]EXPLANATION
We want to find the derivative of:
[tex]f(x)\text{ = }\frac{5}{x}[/tex]To do that, we have to rewrite the fraction in index form:
[tex]f(x)=5x^{-1}[/tex]Now, to differentiate the function with respect to x, we will mutliply the coefficient of x (5) with the power of x (-1) and then subtract 1 from its power.
That is:
[tex]\begin{gathered} f(x)\text{ = 5 }\cdot-1(x^{-1-1}) \\ f(x)=-5x^{-2} \\ \Rightarrow\text{ f(x) = -}\frac{5}{x^2} \end{gathered}[/tex]