Evaluate the Derivative at x=-8 f(x)=-9/x x=-8

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

Find the derivative.

Since $- 9$ is constant with respect to $x$ , the derivative of $- \frac{9}{x}$ with respect to $x$ is $- 9 \frac{d}{d x} [\frac{1}{x}]$ .

$- 9 \frac{d}{d x} [\frac{1}{x}]$

Rewrite $\frac{1}{x}$ as $x^{- 1}$ .

$- 9 \frac{d}{d x} [x^{- 1}]$

Differentiate using the Power Rule which states that $\frac{d}{d x} [x^{n}]$ is $n x^{n - 1}$ where $n = - 1$ .

$- 9 (- x^{- 2})$

Multiply $- 1$ by $- 9$ .

$9 x^{- 2}$

Simplify.

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$9 \frac{1}{x^{2}}$

Combine $9$ and $\frac{1}{x^{2}}$ .

$\frac{9}{x^{2}}$

Replace the variable $x$ with $- 8$ in the expression.

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

Raise $- 8$ to the power of $2$ .

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