1. The problem is to understand how to differentiate a function, which means finding its derivative. 2. Differentiation is the process of finding the rate at which a function changes at any point. 3. The derivative of a function $f(x)$ is denoted as $f'(x)$ or $\frac{df}{dx}$. 4. The basic rule for differentiating a power function $x^n$ is: $$\frac{d}{dx} x^n = n x^{n-1}$$ 5. For example, to differentiate $f(x) = x^3$, apply the rule: $$f'(x) = 3x^{3-1} = 3x^2$$ 6. For sums, differentiate each term separately: If $f(x) = x^3 + 2x$, then $$f'(x) = 3x^2 + 2$$ 7. For constants, the derivative is zero: $$\frac{d}{dx} c = 0$$ where $c$ is a constant. 8. More complex functions require additional rules like the product rule, quotient rule, and chain rule. 9. In summary, differentiation involves applying these rules step-by-step to find the derivative of any function.