1. Let's start with a simple calculus problem: Find the derivative of the function $f(x) = x^2 + 3x + 5$. 2. The derivative of a function gives the rate at which the function's value changes with respect to $x$. 3. The power rule for derivatives states that if $f(x) = x^n$, then $f'(x) = nx^{n-1}$. 4. Applying the power rule to each term: - The derivative of $x^2$ is $2x$. - The derivative of $3x$ is $3$. - The derivative of a constant $5$ is $0$. 5. Therefore, the derivative of the function is: $$f'(x) = 2x + 3$$ 6. This means the slope of the function $f(x)$ at any point $x$ is $2x + 3$. Final answer: $$f'(x) = 2x + 3$$