P1.4 - Differentiation

The derivative of f(x) as the dy For example, knowledge that is the rate of change of y gradient of the tangent to the graph dx of y = f(x) at a point; the gradient of with respect to x.; Knowledge of the chain rule is not the tangent as a limit; interpretation required. as a rate of change; second order derivatives.; The notation f ′(x) and f ′′(x) may be used.

Use derivative as gradient and rate of change to connect the rule to the data and decision in the question.

This matters because derivative as gradient and rate of change determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply derivative as gradient and rate of change to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Derivative as gradient and rate of change is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Differentiation of xn, and related The ability to differentiate expressions such as sums, differences and constant x2 +5x −3 (2x + 5)(x − 1) and is expected. multiples. 3 x.

Use differentiating powers of x to connect the rule to the data and decision in the question.

This matters because differentiating powers of x determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply differentiating powers of x to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Differentiating powers of x is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Applications of differentiation to Use of differentiation to find equations of tangents and gradients, tangents and normals. normals at specific points on a curve.

Use tangents, normals and gradients to connect the rule to the data and decision in the question.

This matters because tangents, normals and gradients determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply tangents, normals and gradients to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Tangents, normals and gradients is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.