Question

Find the derivative of f(x) = negative 9 divided by x at x = -8.

Answer 1

Answer:

$f'(-8)=\frac{9}{64}$

Step-by-step explanation:

Given the function

$f(x)=\frac{-9}{x}$

We can rewrite it as

$f(x)=-9x^{-1}$

Now we can apply the power rule

$f'(x)=9x^{-2}$

Now we can rewrite it

$f'(x)=\frac{9}{x^{2} }$

Now we can plug in x=-8

$f'(-8)=\frac{9}{(-8)^{2} }\\f'(-8)=\frac{9}{64}$