BitWithBite
Mathematics Worksheet
⛓️ Chain Rule
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Recognise composite functions.Apply the chain rule d/dx f(g(x)) = f′(g(x))·g′(x).Differentiate powers, exponentials, logs and trig of an inner function.Combine the chain rule with other differentiation rules.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1d/dx[(4x − 3)6] = ?
2The chain rule d/dx[f(g(x))] equals:
3d/dx[sin(5x)] = ?
4d/dx[e^(−2x)] = ?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5Chain rule: d/dx[f(g(x))] = f′(g(x))·.
6d/dx[sin(5x)] = .
7Differentiate y = (4x − 3)6.
8Differentiate y = sin(5x).
9Differentiate y = (x3 + 2)2.
🚀 Section C · Challenge ● CHALLENGE 5
10Differentiate y = e^(−2x).
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-B 2-C 3-B 4-B | 5 g′(x) 6 5 cos(5x) 7 = 24(4x − 3)5 8 = 5cos(5x) 9 = 6x2(x3 + 2) | 10 = −2e^(−2x)