Question

1. ( f(x) = 3x^2 - 2x )

Explanation:

Assuming we need to find the derivative of \( f(x) = 3x^2 - 2x \) (a common calculus task):

Step 1: Apply power rule to \( 3x^2 \)

The power rule is \( \frac{d}{dx}(x^n) = nx^{n - 1} \). For \( 3x^2 \), \( n = 2 \), so \( \frac{d}{dx}(3x^2)=3\times2x^{2 - 1}=6x \).

Step 2: Apply power rule to \( -2x \)

For \( -2x \), \( n = 1 \), so \( \frac{d}{dx}(-2x)=-2\times1x^{1 - 1}=-2 \).

Step 3: Combine results

The derivative \( f^\prime(x) \) is the sum of the derivatives of each term: \( f^\prime(x)=6x - 2 \).

Answer:

The derivative of \( f(x) = 3x^2 - 2x \) is \( f^\prime(x)=6x - 2 \) (if finding derivative; adjust based on actual problem, e.g., if finding roots: solve \( 3x^2 - 2x = 0 \), \( x(3x - 2)=0 \), so \( x = 0 \) or \( x=\frac{2}{3} \)).