if y = 5x + 4/x^4, find dy/dx at x = 1. the value of dy/dx at x = 1 is . (simplify your answer.)

Explanation:

Step1: Rewrite the function

Rewrite $y = 5x+\frac{4}{x^{4}}$ as $y = 5x + 4x^{-4}$.

Step2: Differentiate term - by - term

Using the power rule $\frac{d}{dx}(ax^{n})=nax^{n - 1}$, for the first term $\frac{d}{dx}(5x)=5$, and for the second term $\frac{d}{dx}(4x^{-4})=4\times(-4)x^{-4 - 1}=-16x^{-5}$. So, $\frac{dy}{dx}=5-16x^{-5}$.

Step3: Substitute x = 1

Substitute $x = 1$ into $\frac{dy}{dx}$. When $x = 1$, $\frac{dy}{dx}=5-16\times1^{-5}=5 - 16=-11$.

Answer:

$-11$