A-Level Differentiation Revision
Differentiation revision for A-Level and International A-Level Maths
This is a free differentiation revision engine for A-Level Maths. Rather than working through a fixed list of past paper questions, it generates a new question every time, marks your answer instantly, and records which topics you have mastered on your skill tree. Because the questions are generated rather than stored, you cannot run out of practice and you cannot learn the answers by heart — which is the usual problem with revising from the same worksheet twice. The engine covers the full differentiation content of Edexcel A-Level Maths and the International A-Level (iAL) Pure 1 to Pure 4 papers, and is equally suitable for AQA, OCR and IB students revising calculus.
What this differentiation revision engine covers
Thirteen topics, from the first introduction to the gradient function through to the Year 13 calculus techniques:
Basic differentiation — the power rule, negative and fractional indices, expanding and dividing before you differentiate Differentiation from first principles — the limit definition, expanding f(x + h), and simplifying the difference quotient Tangents and normals — finding the gradient at a point and forming the equation of the tangent or the normal Second derivatives and stationary points — locating stationary points and classifying them as maxima or minima Increasing and decreasing functions — solving gradient inequalities to find where a curve rises or falls The chain rule — differentiating a function of a function, including brackets raised to a power The product rule — differentiating two functions multiplied together, and factorising the result The quotient rule — differentiating one function divided by another, and when to divide out instead Standard functions — differentiating sin x, cos x, eˣ, ln x and related forms Reciprocal trigonometric functions — the derivatives of sec x, cosec x, cot x and tan x Implicit differentiation — curves not written as y in terms of x, including circles Parametric differentiation — curves given in terms of a parameter, and eliminating it to find the Cartesian equation Connected rates of change — linking two rates together with the chain rule in applied problems
How to use it
Choose either a single topic or a whole exam module. Type your answer and the engine marks it straight away — it compares your expression with the correct derivative mathematically, so any equivalent form is accepted. Writing the same answer as a surd, a fraction or a negative index all count as correct. Every question has a two-step hint ladder if you get stuck. The first hint names the technique, the second nudges you through the method, and neither gives away the answer, so you still have to do the thinking. If you sign in, your accuracy on each topic is saved to your A-Level skill tree, and the engine records which specific error you made rather than simply marking the question wrong.
Differentiation formulas you need to know
The power rule. If y = xⁿ then dy/dx = nxⁿ⁻¹. Multiply by the index, then reduce the index by one. Constants. The derivative of a constant is zero, so a number on its own disappears. The chain rule. If y is a function of u and u is a function of x, then dy/dx = (dy/du) × (du/dx). The product rule. If y = uv then dy/dx = u(dv/dx) + v(du/dx). The quotient rule. If y = u/v then dy/dx = [v(du/dx) − u(dv/dx)] ÷ v². Standard results. sin x differentiates to cos x, cos x to −sin x, tan x to sec² x, eˣ to itself, and ln x to 1/x. These hold only when angles are measured in radians. Stationary points. Solve dy/dx = 0. A positive second derivative means a minimum; a negative one means a maximum.
Common mistakes in differentiation
Most marks lost in differentiation questions come from a small number of repeated errors: multiplying by the index but forgetting to reduce it, substituting a value before differentiating, using the tangent gradient when the question asked for the normal, and forgetting the inside derivative in the chain rule. We have written up the eight most frequent ones, with worked examples of both the wrong and the right answer, in our guide to the differentiation mistakes that cost marks.
More A-Level Maths revision
Differentiation is one of eight A-Level revision engines on eClassroom. If you are revising calculus as a whole, the integration revision engine is the natural companion, since many integration questions are differentiation run backwards. You can see every topic and track your progress across all of them on the revision hub. All of our revision engines are free to use. If you would like help from a tutor as well, you can book a free lesson with an eClassroom maths tutor.