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Level 10 · Calculus · for questions like “A square's sides grow 2 cm each second. How fast is the area growing when the sides are 5 cm?”

💡 The idea

When one thing changes over time, things that depend on it change too. Take the derivative of the formula with respect to time.

• Square: A = s², so dA/dt = 2s × ds/dt
• Cube: V = s³, so dV/dt = 3s² × ds/dt

✏️ Worked examples

1. Square, sides growing 2 cm/s, at side 5: 2 × 5 × 2 = 20 sq cm per second.

2. Cube, edges growing 1 cm/s, at edge 4: 3 × 16 × 1 = 48 cubic cm per second.

⚠️ Watch out

• Put the numbers in after taking the derivative, not before.

🎯 Try these

1. Square, sides growing 3 cm/s, at side 10
2. Cube, edges growing 2 cm/s, at edge 3
3. Square, sides growing 1 cm/s, at side 8

Answers: 1) 60 2) 54 3) 16

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