Differentiation

The topic on one screen

• First principles is on the spec and keeps appearing: $f'(x) = \lim_{h \to 0} \dfrac{f(x + h) - f(x)}{h}$. Learn the structure, not just the answer.
• Differentiation from first principles for $\sin x$ and $\cos x$ uses the compound-angle formula plus the small-$h$ limits — both are given in the question when needed.
• Product, quotient and chain rules: most marks die on sloppy bracketing, not on the rule itself.
• Tangents and normals: gradient at the point first, then $y - y_1 = m(x - x_1)$. The normal gradient is $-\dfrac{1}{m}$.
• Connected rates of change: write down $\dfrac{dV}{dt} = \dfrac{dV}{dr} \times \dfrac{dr}{dt}$ (chain rule) BEFORE substituting anything.
• Increasing/decreasing and stationary points: set $f'(x) = 0$, then justify the nature with $f''$ or a sign check.

Where students actually lose marks

Try it — exam-style

Questions are written in the style of past Edexcel papers (source shown on each) — never copied from them.

Drill it properly