Question

if y = \frac{1}{5x^{6}}, find \frac{dy}{dx} at x = 1.
the value of \frac{dy}{dx} at x = 1 is .
(simplify your answer.)

Explanation:

Step1: Rewrite the function

$y=\frac{1}{5}x^{-6}$

Step2: Differentiate using power - rule

$\frac{dy}{dx}=\frac{1}{5}\times(-6)x^{-7}=-\frac{6}{5x^{7}}$

Step3: Substitute x = 1

When $x = 1$, $\frac{dy}{dx}=-\frac{6}{5\times1^{7}}=-\frac{6}{5}$

Answer:

$-\frac{6}{5}$