This page gives you the key ideas to recognise before you start a question. The full course then takes you through the method, exam-style practice and fully worked solutions.
Differentiate accurately
Apply the power rule term by term and simplify expressions into a differentiable form first when necessary.
Interpret the derivative
dy/dx is a gradient function. Substituting an x-value gives the gradient of the curve at that point.
Tangents and normals
A tangent uses the derivative gradient. A normal has gradient equal to the negative reciprocal, provided the tangent gradient is non-zero.
Stationary points
Set dy/dx = 0 to locate stationary points, then use the question or further reasoning to determine their nature.
Worked example: tangent gradient
For y = 3x² − 4x + 1:
dy/dx = 6x − 4
At x = 2:
dy/dx = 12 − 4
dy/dx = 8
dy/dx = 6x − 4
At x = 2:
dy/dx = 12 − 4
dy/dx = 8
Common mistakes to avoid
- Differentiating a constant as 1 instead of 0.
- Finding dy/dx but forgetting to substitute the required x-value.
- Using the tangent gradient for the normal without taking the negative reciprocal.