Derivative Rules Made Easy | Calculus 1 | Power, Product, Quotient & Trig Rules Explained

Lesson 4 of the Calculus 1 series — moving from first-principles derivatives to the shortcut rules you'll actually use, plus your first two rules for combining functions. In this session: The power rule: d/dx(xⁿ) = n·xⁿ⁻¹, derived from patterns in earlier first-principles work Derivatives of constants and constant multiples Derivative of sin(x) from first principles → cos(x) All six trig derivatives, and the "add/remove co-, flip the sign" shortcut for remembering them The product rule: d/dx(uv) = u·v′ + v·u′ The quotient rule: d/dx(u/v) = (v·u′ − u·v′) / v² — and how it's really just the product rule in disguise A full worked example combining the quotient rule with polynomial simplification, evaluated at a specific point This builds directly on Lesson 3 (derivatives from first principles) — watch that first if you haven't yet. Next up: the chain rule, one of the most important (and most commonly misunderstood) rules in calculus. Questions or something unclear? Drop a comment below — I read and respond to all of them. #Calculus #CalcOne #Derivatives #ProductRule #QuotientRule #PowerRule #TrigDerivatives #MathTutor #LearnCalculus #APCalculus #APCalcAB #APCalcBC #MathAndEngineeringMadeEasy #CalculusForBeginners #STEM