Question

let ( y=(x - 1)(x + 2) ). find ( dy/dx ).

Explanation:

Step1: Expand the function

$$\begin{align*} y&=(x - 1)(x + 2)\\ &=x^2+2x-x - 2\\ &=x^2+x - 2 \end{align*}$$

Step2: Differentiate term - by - term

Using the power rule $\frac{d}{dx}(x^n)=nx^{n - 1}$, for $y=x^2+x - 2$:

• The derivative of $x^2$ is $2x$ (since $n = 2$ in $\frac{d}{dx}(x^n)$).
• The derivative of $x$ is $1$ (since $n = 1$ in $\frac{d}{dx}(x^n)$).
• The derivative of the constant $-2$ is $0$.

So, $\frac{dy}{dx}=2x + 1$.

Answer:

$2x + 1$ (corresponding to the purple - colored option)