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Mathematics Worksheet
🧩 Partial Derivatives
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Compute partial derivatives by treating the other variables as constants.Interpret fx and fy as slopes in the x- and y-directions.Find first-order partials of multivariable functions.Evaluate partial derivatives at a point.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1fx for f(x,y) = 5x2y + 3y = ?
2fy for f(x,y) = 5x2y + 3y = ?
3To find fx, treat y as a:
4fx for f(x,y) = x3 + xy2 = ?
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5To find fx, treat y as a .
6fx for f(x,y) = 5x2y + 3y = .
7Find fx for f(x,y) = 5x2y + 3y.
8Find fy for f(x,y) = 5x2y + 3y.
9Find fx for f(x,y) = x3 + xy2.
🚀 Section C · Challenge ● CHALLENGE 5
10Find fy for f(x,y) = x3 + xy2.
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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1-A 2-B 3-B 4-A | 5 constant 6 10xy 7 = 10xy 8 = 5x2 + 3 9 = 3x2 + y2 | 10 = 2xy