A-Level Calculus: A Beginner's Guide to Differentiation

Calculus feels intimidating, but differentiation is really just one idea: the rate at which something changes — the gradient of a curve at a point.

The core idea

The derivative tells you the slope of a curve at any point. Where the derivative is zero, the curve is flat — that's how you find maximum and minimum points.

The rules you'll use most

• Power rule: multiply by the power, then reduce the power by one.
• Chain rule: for a function inside a function.
• Product and quotient rules: for things multiplied or divided.

Common beginner mistakes

Forgetting to reduce the power, mishandling negative or fractional powers, and rushing the chain rule are the usual culprits. Slow, clear working fixes all three.

Build intuition, not just mechanics

Always ask what the derivative means in the context of the question. Understanding beats memorising when questions get unfamiliar.