Grade 12 Power Rule Worksheets
Start with eight focused practice problems, then use the answer key below to check the worksheet.
Practice Worksheet
Grade 12 Power Rule Practice
Solve each problem. Show your work.
- 1.Differentiate: f(x) = -4x^5 - 4x^4 + 8
- 2.Differentiate: f(x) = -x^3 + 1x^2
- 3.Differentiate: f(x) = -2x^6 - 4x^3 + 5
- 4.Differentiate: f(x) = -5x^6 + 3x^4 + 7
- 5.Differentiate: f(x) = -4x^6 - 1x^3 - 1
- 6.Differentiate: f(x) = -4x^3 - 2x^2 - 2
- 7.Differentiate: f(x) = 4x^4 + 4x^2 + 3
- 8.Differentiate: f(x) = 2x^4 + 2x^2 + 3
Show answer key
- Question 1: f'(x) = -20x^4 - 16x^3
- Question 2: f'(x) = -3x^2 + 2x^1
- Question 3: f'(x) = -12x^5 - 12x^2
- Question 4: f'(x) = -30x^5 + 12x^3
- Question 5: f'(x) = -24x^5 - 3x^2
- Question 6: f'(x) = -12x^2 - 4x^1
- Question 7: f'(x) = 16x^3 + 8x^1
- Question 8: f'(x) = 8x^3 + 4x^1
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About These Worksheets
Grade 12 students use the power rule as their first efficient derivative shortcut after learning the meaning of derivative.
Power rule worksheets give Grade 12 calculus students repeated practice differentiating powers of x. Students learn that the derivative of x^n is nx^(n - 1), then apply the rule to polynomial terms, constants, radicals rewritten with fractional exponents, and expressions with negative exponents. The rule is quick, but only when exponent notation is handled carefully.
These worksheets include single terms, polynomial functions, tangent slope questions, and simple motion contexts where the derivative represents velocity. Students practise simplifying before differentiating, differentiating term by term, and interpreting the derivative as a rate of change. Power rule fluency is the foundation for product, quotient, and chain rule work because those rules often still require power-rule differentiation inside each step.
Skills Practised
- Differentiating x^n using the power rule
- Applying the rule to polynomial functions
- Using fractional and negative exponents
- Finding slopes of tangents from derivatives
- Interpreting derivatives as rates of change
Parent Tip: Most parents cannot check derivatives confidently. Use the answer key for the final derivative, and use photo checking if exponent simplification or tangent-slope steps are unclear.