1. The problem is to find the derivative of a function, which means determining the rate at which the function's value changes with respect to its input variable. 2. The formula for the derivative of a function $f(x)$ is given by the limit definition: $$f'(x) = \lim_{h \to 0} \frac{f(x+h) - f(x)}{h}$$. 3. Important rules for differentiation include the power rule, product rule, quotient rule, and chain rule, which help differentiate various types of functions. 4. For example, using the power rule, if $f(x) = x^n$, then the derivative is $f'(x) = nx^{n-1}$. 5. Differentiation is a fundamental tool in calculus used to analyze the behavior of functions, such as finding slopes of tangent lines and rates of change. 6. To differentiate a function, apply the appropriate rule based on the function's form and simplify the result to get the derivative.