MathematicsFreePrintable
Derivatives Power Rule Practice
A free mathematics worksheet ready for your classroom. Open in Kuraplan to grab the print-ready PDF, customize it for your students, or generate a fresh version in seconds.
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.
About This Worksheet
Free in Kuraplan
Sign up free, grab the PDF, and customize it for your class.
Print-Ready
Formatted for standard paper. Clean layout, easy to read.
AI-Generated
Created with Kuraplan's AI, designed for real classroom use.
For Teachers & Parents
Use in classrooms, for homework, tutoring, or homeschool.
Need a custom version of this worksheet?
Kuraplan's AI generates custom worksheets in seconds — differentiated for every learner, aligned to your curriculum.
Generate Custom Worksheets — Free No credit card Curriculum-aligned Under 60 seconds
