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Mathematics Worksheet
📐 Differentiation
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After this worksheet you can
Interpret the derivative as the slope of the tangent line and an instantaneous rate.Compute a derivative from the limit definition.Apply the power rule to basic functions.Evaluate a derivative at a specific point.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1If f(x) = x5, then f′(x) = ?
2The derivative of the constant f(x) = −9 is:
3f′(x) gives the ___ of the tangent line.
4The limit definition is f′(x) = lim(h→0) of:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5For f(x) = xn, f′(x) = .
6The derivative of any constant is .
7Find the derivative of f(x) = x5.
8Find the derivative of f(x) = x10.
9Use the limit definition to find the derivative of f(x) = 3x.
🚀 Section C · Challenge ● CHALLENGE 5
10Find f′(3) if f(x) = x3.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-C 3-B 4-A | 5 n·xn−1 6 0 7 = 5x4 8 = 10x9 9 = 3 | 10 = 27