1. The problem is to find the derivative of the function $f(x) = x^2 + 3x$. 2. The derivative of a function $f(x)$, denoted $f'(x)$, represents the rate of change or slope of the function at any point $x$. 3. We use the power rule for derivatives: if $f(x) = x^n$, then $f'(x) = nx^{n-1}$. 4. Applying the power rule to each term: - For $x^2$, the derivative is $2x^{2-1} = 2x$. - For $3x$, the derivative is $3 \cdot x^{1-1} = 3 \cdot x^0 = 3$. 5. Adding these results, the derivative is: $$f'(x) = 2x + 3$$ 6. Therefore, the derivative of $f(x) = x^2 + 3x$ is $f'(x) = 2x + 3$.