Question

find the derivative of the function.
y = (x^3 + 3)/x
dy/dx = □

Explanation:

Step1: Simplify the function

Rewrite $y = \frac{x^{3}+3}{x}$ as $y=x^{2}+\frac{3}{x}=x^{2}+3x^{- 1}$.

Step2: Apply the power - rule for derivatives

The power - rule states that if $y = x^{n}$, then $\frac{dy}{dx}=nx^{n - 1}$.
For $y=x^{2}$, $\frac{d}{dx}(x^{2}) = 2x$.
For $y = 3x^{-1}$, $\frac{d}{dx}(3x^{-1})=3\times(-1)x^{-1 - 1}=-3x^{-2}$.

Step3: Combine the derivatives

$\frac{dy}{dx}=\frac{d}{dx}(x^{2})+\frac{d}{dx}(3x^{-1})=2x-3x^{-2}$.

Answer:

$2x-\frac{3}{x^{2}}$