Free ebookDerivatives from Scratch: Rules, Meaning, and Real-World Rates

Course Description

Derivatives from Scratch: Rules, Meaning, and Real-World Rates is a practical calculus ebook course in the Basic studies category designed to help you understand derivatives with confidence, even if you are starting from zero. You will learn what a derivative really means, how it connects to slopes and graphs, and why it matters in everyday problem solving across science, business, and technology.

You will build understanding progressively by moving from average change to instantaneous rate using the limit definition of the derivative, then connecting that idea to tangent lines, local linearity, and approximation. Along the way, you will interpret derivative meaning in context, such as velocity, growth, and marginal change, so you can translate symbols into real-world insight and communicate results clearly.

Once the concept is solid, you will master core differentiation rules used in calculus, including the power rule, constant and linearity rules, product and quotient rules, and the chain rule for nested functions. You will practice combining rules in multi-step differentiation, simplifying expressions, and checking domains and notation to avoid common pitfalls that slow learners down.

To make calculus useful beyond exercises, the course emphasizes reading derivatives from graphs and data by analyzing sign, magnitude, and curve shapes. You will also learn to model real-world rates and interpret what derivatives say about change, sensitivity, and trends, building skills that transfer directly to academic work and applied problem solving.

Start this free calculus course today and learn derivatives from scratch with clear explanations, meaningful practice, and real-world rates you can use immediately.