Question

find the derivative of the function. y = 5x^2 - 8x - 2x^(-2) dy/dx = □

Explanation:

Step1: Apply power - rule to each term

The power - rule states that if $y = ax^n$, then $\frac{dy}{dx}=nax^{n - 1}$. For $y_1 = 5x^2$, $\frac{dy_1}{dx}=2\times5x^{2 - 1}=10x$. For $y_2=-8x$, $\frac{dy_2}{dx}=-8\times1x^{1 - 1}=-8$. For $y_3=-2x^{-2}$, $\frac{dy_3}{dx}=-2\times(-2)x^{-2 - 1}=4x^{-3}$.

Step2: Sum up the derivatives of each term

Since $y = y_1 + y_2 + y_3$, then $\frac{dy}{dx}=\frac{dy_1}{dx}+\frac{dy_2}{dx}+\frac{dy_3}{dx}$.
$\frac{dy}{dx}=10x-8 + 4x^{-3}$

Answer:

$10x-8+\frac{4}{x^{3}}$