Answer:
The derivative of f'(x) = -9/x when x = 4 is 9/16.
Step-by-step explanation:
We are to find the derivative of [tex]f(x) = \frac{-9}{x}[/tex] and [tex]x= -4[/tex]
[tex]f(x) = \frac{-9}{x} = -9x^{-1}[/tex]
[tex]f'(x) = [f(x)]'[/tex]
[tex]f'(x) = (-9x)^{-1}[/tex]
We know that,
[tex](x^n)' = nx^{n-1} where n is a constant[/tex]
So, [tex]f'(x) = -9(-1)x^{-1-1}[/tex]
[tex]f'(x) = 9x^{-2} = \frac{9}{x^2}[/tex]
Therefore when [tex]x=-4[/tex],
[tex]f'(-4)= \frac{9}{-4^2}[/tex][tex]= \frac{9}{16}[/tex]
Therefore, the derivative of [tex]f'(x)= \frac{-9}{x}[/tex] when [tex]x= -4[/tex] is 9/16.
