P3.4 - Differentiation

Differentiation of ekx, ln kx, sin kx, cos kx, tan kx and their sums and differences.

Use differentiating exp, log and trig functions to connect the rule to the data and decision in the question.

This matters because differentiating exp, log and trig functions determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply differentiating exp, log and trig functions to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Differentiating exp, log and trig functions is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Differentiation using the product Differentiation of cosec x, cot x and sec x are required. rule, the quotient rule and the chain Skill will be expected in the differentiation of functions rule. generated from standard functions using products, quotients and composition, such as e3x 2x4 sin x,, cos x2 and tan2 2x. x.

Use differentiation to connect the rule to the data and decision in the question.

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

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

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

Use dy/dx = 1/(dx/dy), including finding dy/dx when x is given as a function of y.

Use reciprocal derivative relationship to connect the rule to the data and decision in the question.

This matters because reciprocal derivative relationship determines what can be inferred or chosen; begin with the stated conditions and keep the conclusion tied to the evidence.

Example: apply reciprocal derivative relationship to one small, clearly defined case, show the key step or comparison, and explain the result in words.

Boundary: Reciprocal derivative relationship is not a universal recommendation. Check the syllabus scope, assumptions, units and the limits of the evidence before generalising.

Understand and use exponential Students should be familiar with terms such as ‘initial’, growth and decay. ‘meaning when’ t = 0.; Students may need to explore the behaviour for large values of t or to consider whether the range of values predicted is appropriate.; Consideration of a second improved model may be required. d Knowledge and use of the result (ax) = ax ln a is dx expected.

Use exponential to connect the rule to the data and decision in the question.

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

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

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