Calculus Guides
A complete learning path for differentiation, from “what is a derivative?” to real-world applications — written for first-time students and built to pair with the step-by-step calculator.
Part 1
Intro to Derivatives
What a derivative measures, the tangent line picture, the limit definition worked once in full, and how to read prime and Leibniz notation.
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Part 2
Basic Rules: The Power Rule, Constants, and Sums
The four foundational rules — the power rule, constants, constant multiples, and sums — that take any polynomial apart, with a step-by-step method, the classic beginner mistakes, and a full worked example.
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Part 3
Product & Quotient Rules
What to do when functions are multiplied or divided: both rules step by step, when rewriting beats both of them, and the errors to watch for.
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Part 4
Derivatives of Transcendental Functions
The trig cycle, why eˣ is its own derivative, the natural log rule — the short list worth memorizing, and the logic that makes it stick.
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Part 5
Mastering the Chain Rule
Composite functions and the outside-inside method, four fully worked examples including a double chain, and the most common mistake in calculus.
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Part 6
Applications of Derivatives
Where it all gets used: velocity and acceleration, marginal cost, optimization, medicine, and the derivative hiding in your speedometer.
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Review
7 Common Derivative Mistakes (and How to Avoid Them)
The errors graders see most — each shown wrong and right side by side, with the checking habits that catch them.
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