Derivative as gradient
Move from average gradient on a secant line to the instantaneous gradient on a tangent.
03 · Content engine
A five-minute lesson with a clear next step.
This Grade 12 Differential Calculus sample demonstrates the content direction: calm worked examples, speech-friendly explanations and a direct connection between concept, calculation and graph.
Lesson arcGradient → rule → graph.
Derivative meaning, the power rule, tangent equations and stationary points connect through one cubic example.
Sample lesson
Grade 12 Differential Calculus
The lesson includes English subtitles and native browser playback. Use full screen for the clearest view of the mathematics.
Inside the lesson
Four connected ideas, one worked example.
The sample is designed to be short enough for revision and structured enough to lead into practice.
Power rule
Differentiate polynomial terms efficiently and connect the rule to the derivative function.
Tangent equation
Use a point and a gradient to write the equation of a tangent line.
Stationary points
Set the derivative to zero, calculate the points and classify the turning behaviour.
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