Product & Quotient Rules Worksheet 9

Differentiate functions exactly, state necessary domains and check the resulting symbolic expression.

hard: Use another set to practice explaining and checking your answers.

27 problems · 25-30 minutes · Skills: derivatives, product rule, quotient rule

About This Worksheet

This hard-level worksheet contains 27 problems designed for 12th Grade students practicing product & quotient rules. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

Manipulate algebraic expressions and understand functions, limits and derivative notation.

Differentiate functions exactly, state necessary domains and check the resulting symbolic expression.
Check your result using the method in the example before moving to the next question.

How to Solve: Worked Example

Example Problem: Differentiate with respect to x: f(x) = (x+4)·(x^2+7).

Solution Steps:

Use (uv)′ = u′v + uv′.
Expand and combine like terms.

Answer: f′(x) = 3·x^2+8·x+7

Tip: Check your result using the method in the example before moving to the next question.

Paper Include separate answer key in PDF

Differentiate with respect to x: f(x) = (x+2)·(x^2+1).

Differentiate with respect to x: f(x) = (4·x+4)/(x+8).

Differentiate with respect to x: f(x) = (x+1)·(x^2+1).

Differentiate with respect to x: f(x) = (4·x+5)/(x+6).

Differentiate with respect to x: f(x) = (x+1)·(x^2+5).

Differentiate with respect to x: f(x) = (6·x+6)/(x+8).

Differentiate with respect to x: f(x) = (x+1)·(x^2+3).

Differentiate with respect to x: f(x) = (6·x+7)/(x+4).

Differentiate with respect to x: f(x) = (x+1)·(x^2+8).

Differentiate with respect to x: f(x) = (3·x+6)/(x+8).

Differentiate with respect to x: f(x) = (x+7)·(x^2+1).

Differentiate with respect to x: f(x) = (5·x+2)/(x+2).

Differentiate with respect to x: f(x) = (x+8)·(x^2+7).

Differentiate with respect to x: f(x) = (3·x+5)/(x+4).

Differentiate with respect to x: f(x) = (x+1)·(x^2+6).

Differentiate with respect to x: f(x) = (8·x+8)/(x+7).

Differentiate with respect to x: f(x) = (x+4)·(x^2+2).

Differentiate with respect to x: f(x) = (2·x+2)/(x+5).

Differentiate with respect to x: f(x) = (x+4)·(x^2+3).

Differentiate with respect to x: f(x) = (2·x+9)/(x+4).

Differentiate with respect to x: f(x) = (x+6)·(x^2+2).

Differentiate with respect to x: f(x) = (5·x+1)/(x+3).

Differentiate with respect to x: f(x) = (x+6)·(x^2+7).

Differentiate with respect to x: f(x) = (1·x+8)/(x+6).

Differentiate with respect to x: f(x) = (x+6)·(x^2+4).

Differentiate with respect to x: f(x) = (7·x+4)/(x+3).

Differentiate with respect to x: f(x) = (x+5)·(x^2+1).

Answer Key

1. f′(x) = 3·x^2+4·x+12. f′(x) = (28)/(x+8)^23. f′(x) = 3·x^2+2·x+14. f′(x) = (19)/(x+6)^25. f′(x) = 3·x^2+2·x+56. f′(x) = (42)/(x+8)^27. f′(x) = 3·x^2+2·x+38. f′(x) = (17)/(x+4)^29. f′(x) = 3·x^2+2·x+810. f′(x) = (18)/(x+8)^211. f′(x) = 3·x^2+14·x+112. f′(x) = (8)/(x+2)^213. f′(x) = 3·x^2+16·x+714. f′(x) = (7)/(x+4)^215. f′(x) = 3·x^2+2·x+616. f′(x) = (48)/(x+7)^217. f′(x) = 3·x^2+8·x+218. f′(x) = (8)/(x+5)^219. f′(x) = 3·x^2+8·x+320. f′(x) = (-1)/(x+4)^221. f′(x) = 3·x^2+12·x+222. f′(x) = (14)/(x+3)^223. f′(x) = 3·x^2+12·x+724. f′(x) = (-2)/(x+6)^225. f′(x) = 3·x^2+12·x+426. f′(x) = (17)/(x+3)^227. f′(x) = 3·x^2+10·x+1

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This worksheet focuses on derivatives, product rule, quotient rule. It is designed for 12th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

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This worksheet contains 27 problems. It typically takes 25-30 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.