Pure 2 differentiation
Understand a changing gradient, choose a differentiation rule and interpret the result.
Start with sine and cosine: compare chord and tangent gradients, then work through the proofs and applications. Then study exponential and logarithmic derivatives, domains, tangents and rates. Use the chain rule to connect the derivatives of nested functions. More differentiation lessons are being added.
- Differentiating sin and cosUnderstand why sin x differentiates to cos x and cos x to −sin x. Explore chord and tangent gradients, first-principles proofs, radian units and original worked practice.
- Differentiating exponentials and logarithmsDifferentiate eˣ, aˣ and natural logarithms with clear domain checks. Compare function and derivative graphs, find tangents and interpret original growth and decay models.
- Chain ruleLearn the chain rule for composite functions, including powers, roots, trigonometric functions, exponentials and logarithms. Choose each layer yourself, then practise with full worked solutions.
- Derivatives of inverse functionsDifferentiate inverse functions using reciprocal gradients at corresponding points. Learn when dy/dx = 1/(dx/dy) is valid, keep the correct branch and handle zero-gradient exceptions.
- Product ruleUnderstand and apply the product rule with a changing-area explorer, original worked examples and independent practice. Combine it with the chain rule, factorise derivatives and solve tangent and stationary-point problems.
- Quotient ruleLearn the quotient rule, including the subtraction order, squared denominator and original domain. Compare the two contributions to a quotient’s gradient, then practise with worked solutions.
- Differentiating tan, sec, cosec and cotDerive and use the derivatives of tan, sec, cosec and cot. Explore one branch at a time, combine rules for composite expressions and practise exact tangents and stationary points.
- Differentiating inverse trigonometric functionsDerive the derivatives of arcsin, arccos and arctan with correct branches and domains. Practise composite functions, products, quotients and tangents, with an extension on reciprocal inverse functions.
- Parametric differentiationFind dy/dx from parametric equations using dy/dt divided by dx/dt. Explore horizontal and vertical tangents, chain rules and points where both parameter derivatives vanish.