Differentiation in IGCSE Add Math: Exam Technique That Scores

If you can only be excellent at one thing in 0606, make it differentiation. It is the core of calculus, the syllabus’s largest topic, and it leaks into tangents, stationary points, rates of change and kinematics on both papers. Here is the technique as we teach it, mark scheme first.

The three rules as written routines

Product rule, for $y = uv$. Before differentiating anything, write the setup:

$u = x^2$, $u' = 2x$; $v = \sin x$, $v' = \cos x$ $\frac{dy}{dx} = u'v + uv' = 2x \sin x + x^2 \cos x$

That setup line is not decoration, in a typical 3-mark product-rule question, identifying $u$, $u'$, $v$, $v'$ correctly is the first method mark. Skipping to the answer risks all three marks on one slip.

Quotient rule, for $y = \frac{u}{v}$: $\frac{dy}{dx} = \frac{u'v - uv'}{v^2}$. The order of the numerator matters (top times derivative-of-bottom is the subtracted term), and the most common error in scripts is a sign slip there. Write the formula as a general statement first, every time.

Chain rule, for composite functions like $y = (3x^2 - 5)^4$: identify the inside, differentiate the outside, multiply by the derivative of the inside:

$\frac{dy}{dx} = 4(3x^2 - 5)^3 \times 6x = 24x(3x^2 - 5)^3$

For $e^{f(x)}$, $\ln(f(x))$, $\sin(f(x))$ the pattern is identical, outer derivative $\times$ inner derivative.

The standard derivatives you must carry

$x^n \to nx^{n-1}$ · $\sin x \to \cos x$ · $\cos x \to -\sin x$ · $\tan x \to \sec^2 x$ · $e^x \to e^x$ · $\ln x \to \frac{1}{x}$. None of these are given in the exam, they’re part of the memorise list. On the non-calculator Paper 1 they must be instant.

Where the marks actually live: applications

Pure “differentiate this” questions are the warm-up. The real marks come from applications, each with its own routine:

• Tangents and normals: differentiate, substitute $x$, that’s the tangent gradient $m$ (normal: $-\frac{1}{m}$), $y - y_1 = m(x - x_1)$. Examiners report every session that students find the right gradient and then use the wrong one.
• Stationary points: set $\frac{dy}{dx} = 0$ and write that line down. "$\frac{dy}{dx} = 0$" is routinely a B or M mark by itself. Solve, then classify with the second derivative, stating the conclusion in words (”$\frac{d^2y}{dx^2} = -6 < 0$, hence maximum”).
• Connected rates: write the chain $\frac{dy}{dt} = \frac{dy}{dx} \times \frac{dx}{dt}$ before substituting numbers. The chain statement is the method mark.
• Kinematics: $v = \frac{ds}{dt}$, $a = \frac{dv}{dt}$. State the relationship before computing.

The common thread: state the general relationship, then substitute. 0606 mark schemes are built to reward visible method, and differentiation questions are the clearest example in the whole syllabus.

A 2-week sharpening plan

Days 1–4: drill the three rules on mixed expressions, ten a day, with full setup lines. Days 5–8: tangents/normals and stationary points from past papers. Days 9–12: rates of change and kinematics. Days 13–14: one full mixed exercise per day, marked against real mark schemes, log every dropped mark by cause. Slot this inside the 8-week revision plan if you’re further out from the exam.

Differentiation is also the topic where 1-to-1 feedback pays back fastest, because most lost marks are working habits, invisible to the student. Teacher Rig has spent 8 years marking exactly these scripts, book the free 1-hour trial class on WhatsApp and bring your hardest past-paper question.