Grade 12 Product and Quotient Rule Worksheets
Start with eight focused practice problems, then use the answer key below to check the worksheet.
Practice Worksheet
Grade 12 Product and Quotient Rule Practice
Solve each problem. Show your work.
- 1.Differentiate: f(x) = (4x + 4)(x + 1)
- 2.Differentiate: f(x) = (5x - 2)(4x - 3)
- 3.Differentiate: f(x) = (x - 3) / (x - 6)
- 4.Differentiate: f(x) = (2x - 1) / (x + 3)
- 5.Differentiate: f(x) = (x + 3) / (5x - 4)
- 6.Differentiate: f(x) = (3x - 3)(3x + 3)
- 7.Differentiate: f(x) = (4x)(5x - 5)
- 8.Differentiate: f(x) = (2x - 3)(3x - 1)
Show answer key
- Question 1: f'(x) = 8x + 8
- Question 2: f'(x) = 40x - 23
- Question 3: f'(x) = -3/(x - 6)^2
- Question 4: f'(x) = 7/(x + 3)^2
- Question 5: f'(x) = -19/(5x - 4)^2
- Question 6: f'(x) = 18x
- Question 7: f'(x) = 40x - 20
- Question 8: f'(x) = 12x - 11
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About These Worksheets
Grade 12 students apply product and quotient rules after mastering basic derivative rules and before tackling longer application problems.
Product and quotient rule worksheets help Grade 12 students differentiate functions that are multiplied or divided, where the power rule alone is not enough. Students learn that the derivative of a product is not simply the product of the derivatives, and that quotient rule requires careful ordering of terms in the numerator. These rules reward organized notation.
The worksheets include products of polynomials, polynomial-radical products, rational functions, and mixed questions where students must decide which rule applies. Students practise labelling u and v, finding each derivative, substituting into the rule, and simplifying the result. Product and quotient rule fluency is essential for curve sketching, optimization, related rates, and derivative questions involving rational expressions in senior math.
Skills Practised
- Choosing between product rule and quotient rule
- Labelling u and v before differentiating
- Applying product rule to multiplied functions
- Applying quotient rule to rational functions
- Simplifying derivative expressions
Parent Tip: These solutions are difficult to inspect casually. Use the answer key for the derivative, and ask for photo checking when your teen needs help finding where a sign or ordering error occurred.