Question

if (y = \frac{1}{x^{9}}), find (\frac{dy}{dx}) at (x=-2).
the value of (\frac{dy}{dx}) at (x = - 2) is (square).
(simplify your answer.)

Explanation:

Step1: Rewrite the function

$y = x^{-9}$

Step2: Differentiate using power - rule

$\frac{dy}{dx}=-9x^{-10}=-\frac{9}{x^{10}}$

Step3: Substitute x = - 2

$\frac{dy}{dx}\big|_{x = - 2}=-\frac{9}{(-2)^{10}}=-\frac{9}{1024}$

Answer:

$-\frac{9}{1024}$