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.

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