Calculus practice
Symbolic Differentials worksheets
Find exact symbolic differentials for polynomial, rational, composite, and trigonometric functions with fully worked rule-specific keys.
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For each function, find the exact differential dy = f'(x) dx. Keep the full derivative grouped as the coefficient of dx.
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Customize this worksheetKeep the whole derivative attached to dx
Each answer names the rule, shows the exact derivative, and finishes with the entire expression grouped in dy = (f'(x)) dx.
Learning objective
What this activity builds
Differentiate exactly and write the complete derivative as the grouped coefficient of dx in dy = f'(x) dx.
Worked example
Find dy when y = (x^2 + 1)^3.
dy = (6x(x^2 + 1)^2) dx.
Differentiate the outer power, multiply by the inner derivative 2x, and group the whole result before dx.
Teaching notes
Make the practice count
- Write f'(x) first, then place the whole derivative in parentheses before dx.
- Name numerator and denominator before applying the quotient rule.
- Retain restrictions from the original function even after simplifying its derivative.
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Choose 8, 10, or 12 problems and any nonempty selection of polynomial, rational, composite, and trigonometric functions. Every answer remains exact.