## Syllabus • Differentiation

Topic | Differentiation |

Module | C1 |

Description |
The derivative of f(x) as the gradient of the tangent
to the graph of y = f (x) at a point; the gradient of the
tangent as a limit; interpretation as a rate of change;
second order derivatives. For example, knowledge that is
the rate of change of y with respect
to x. Knowledge of the chain rule is
not required. Differentiation of \(x^n\), and related sums and differences. For example, for \(n > 1\), the ability to differentiate expressions such as \[(2x + 5)(x - 1)\] and \[\frac{(x^2+5-3)}{3x^{1/2}}\] is expected. Applications of differentiation to gradients, tangents and normals. Use of differentiation to find equations of tangents and normals at specific points on a curve. |