Question

q4
1 point
compute the derivative of $f(x)$ algebraically.
$f(x)=x^2 - 2$
$\bigcirc$ $f(x)=2$
$\bigcirc$ $f(x)=2x - 2$
$\bigcirc$ $f(x)=2x^2$
$\bigcirc$ $f(x)=2x$

Explanation:

Step1: Differentiate $x^2$ term

Use power rule: $\frac{d}{dx}(x^n)=nx^{n-1}$. For $n=2$, $\frac{d}{dx}(x^2)=2x^{2-1}=2x$

Step2: Differentiate constant term

Derivative of constant $c$ is 0: $\frac{d}{dx}(-2)=0$

Step3: Sum the results

Add derivatives of each term: $f'(x)=2x+0$

Answer:

$f'(x)=2x$ (matches the last option)