Students determine derivatives from first principles using the difference quotient and apply linearity, power, trigonometric, exponential, and logarithmic differentiation rules to familiar functions, including appropriate domains and radians for trigonometric functions. They differentiate products, quotients, and composite functions using the product, quotient, and chain rules, including standard algebraic, trigonometric, exponential, and logarithmic combinations. They compute second, third, and higher-order derivatives when patterns are clear, interpreting the second derivative through concavity and acceleration while excluding multivariable, inverse, hyperbolic, variable-base, and advanced generalized differentiation.