Differentiate from first principles when asked, apply the power rule everywhere else, and know what a derivative actually tells you about a graph.
By the end, you can
differentiate using first principles and the rules, and interpret a derivative as a gradient or rate of change.
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Derivatives — First Principles and the Rules
One idea, two questions
A derivative answers two questions at once: how steep is this curve here? and how fast is this quantity changing? 📐
They are the same question. Gradient is rate of change — metres per second, rand per item, degrees per minute. Once that clicks, word problems in calculus stop being a separate topic.
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Derivatives — First Principles and the Rules
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Read a parabola or exponential graph properly — intercepts, turning point, asymptotes, domain and range — and find an inverse without guessing.
Work with the common ratio, find any term or sum, and know exactly when an infinite series converges and when it does not.
Turn a word problem into one equation, differentiate it to find the maximum or minimum, and interpret rates of change in real units.
Apply the addition rule, tell independent from mutually exclusive, read a Venn or tree diagram, and count arrangements without listing them.
Solve linear and non-linear systems by substitution, keep your ordered pairs matched, and handle the exponent-law questions that look harder than they are.
The whole Mathematics P1 path → All High School MicroQuests → Browse all 134 →
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Derivatives — First Principles and the Rules
R19 · 13 min · certificate
