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Derivatives Power Rule Practice
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Derivatives Power Rule Practice Paper 1
📚 Part 1: Power Rule Application
Success Criteria: Apply the power rule f'(x) = nax^(n-1) correctly
1. Find the derivative of f(x) = 3x⁴
2. Find the derivative of f(x) = -5x²
3. Differentiate g(x) = 7x³
4. Find f'(x) if f(x) = 2x⁵ - 6x³ + 4x
5. What is the derivative of h(x) = x⁶ + 8x² - 3?
🎯 Part 2: Conceptual Understanding
Success Criteria: Explain the meaning of derivatives as rates of change
6. A car's position is given by s(t) = 4t³ metres after t seconds. What does s'(t) represent?
The car's positionThe car's velocityThe car's accelerationThe distance travelled
7. Find the velocity function if s(t) = 4t³
8. In your own words, explain what a derivative tells us about a function:
⚡ Part 3: Extension Challenge
Success Criteria: Apply power rule to negative and fractional exponents
9. Challenge: Find the derivative of f(x) = 4x⁻²
10. Extension: If f(x) = 3x⁻¹ + 2x⁻³, find f'(x)
11. Real-world Application: The number of bacteria in a culture is given by N(t) = 100t² + 50t, where t is time in hours. Find the rate of bacterial growth at any time t.
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