Calculus practice
Higher Order Derivatives worksheets
Differentiate exact sparse power sums through the second, third, fourth or fifth derivative using prime or Leibniz notation.
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Differentiate each function through the requested order. Keep coefficients and powers exact, and state the valid real domain at every stage.
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Customize this worksheetFollow the power rule through every requested stage
Each worked key keeps exact coefficients, exact powers and the real domain visible from the original function through the final derivative.
Learning objective
What this activity builds
Apply the power rule repeatedly and track the real domain through a requested derivative order.
Worked example
Find the third derivative of f(x) = 2x^4 - x.
f'(x) = 8x^3 - 1, f''(x) = 24x^2, and f'''(x) = 48x.
Apply the power rule one stage at a time; a constant disappears at the next derivative.
Teaching notes
Make the practice count
- Write every intermediate derivative before the requested answer.
- Keep fractional coefficients and exponents exact.
- Do not restore excluded domain points after simplification.
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Choose 8, 10, or 12 problems, any nonempty selection of derivative orders 2 through 5, integer or fractional powers, and prime, Leibniz, or mixed notation.