Answer:
9/16
Step-by-step explanation:
[tex]f(x)=-\frac{9}{x}[/tex]
[tex]f(x)=-9x^{-1}[/tex]
Derivative rule:
[tex]f(x)=x^{n} \\[/tex]
[tex]\frac{df}{dx}=nx^{n-1}[/tex]
Here, n=-1, so
[tex]\frac{df}{dx}=(-9)(-1)x^{-2} =\frac{9}{x^{2} }[/tex]
Evaluating this at x=-4 gives 9/16
