Calculus practice
Logarithmic Differentiation worksheets
Differentiate variable powers, products and quotients with exact real-domain guidance.
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Differentiate each function using logarithmic differentiation. State the real domain used by the logarithmic derivative formula.
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Customize this worksheetTurn powers and factors into sums
Each worked key shows the logarithm step, the logarithmic derivative, and the final substitution of the original function.
Learning objective
What this activity builds
Take logarithms, differentiate the expanded logarithm, and multiply by the original function.
Worked example
Differentiate y = x^x for x > 0.
dy/dx = x^x(ln(x) + 1).
Write ln(y) = x ln(x), differentiate to get y'/y = ln(x) + 1, then multiply by y.
Teaching notes
Make the practice count
- Use ln|f| for fixed real powers so negative nonzero function values are retained.
- A variable-power base must stay positive.
- Check numerator zeros separately when the logarithmic formula has a removable-looking 0/0.
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Choose 8, 10, or 12 problems, any nonempty selection of variable powers, products and quotients, and prime, Leibniz or mixed notation.