Question

if y = 5x + \frac{4}{x^{3}}, 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

$y = 5x+4x^{-3}$

Step2: Differentiate term - by - term

$\frac{dy}{dx}=5 - 12x^{-4}$

Step3: Substitute x = 1

$\frac{dy}{dx}\big|_{x = 1}=5-12(1)^{-4}=5 - 12=-7$

Answer:

$-7$