StellarAfter learning the power rule, students next combine it with several basic derivative rules. The derivative of a constant is 0 because a constant function does not change. The derivative of a sum is the sum of the derivatives, the derivative of a difference is the difference of the derivatives, and the derivative of a constant multiple is the constant times the derivative of the function. These rules make differentiation practical because they allow us to break larger expressions into smaller pieces and differentiate each part separately.
These rules are essential for polynomial differentiation and for nearly every derivative students compute in early calculus. Instead of re-deriving everything from the definition, we use structure. If a function is made of several terms added together, we can differentiate each term on its own and then recombine the results. This helps students see derivatives as something systematic and predictable rather than a collection of unrelated tricks.