Worksheets · Calculus

Quotient rule worksheet

Bottom times the derivative of the top, minus top times the derivative of the bottom, all over the bottom squared. The order of that subtraction matters, which is why it is worth saying out loud.

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Sigma Prep · sigmaprep.io/worksheets

Name

The Quotient Rule

Date Period

Differentiate each function.

  1. f(x)=x2+92x+7
  2. f(x)=−5x2−5−2x−2
  3. f(x)=−x2−7−x−4
  4. f(x)=4x2−23x+2
  5. f(x)=3x2+9−4x−3
  6. f(x)=−2x2−7x−1
  7. f(x)=5x2−92x−7
  8. f(x)=5x2+94x−1
  9. f(x)=2x2+53x−7
  10. f(x)=x2+2−x−3
  11. f(x)=3x2+14x−2
  12. f(x)=−5x2−23x−2
  13. f(x)=−x2−7x+5
  14. f(x)=−4x2−94x−2
  15. f(x)=−5x2−7x−8
  16. f(x)=4x2−1−2x+3
  17. f(x)=2x2+83x−4
  18. f(x)=−2x2−9x−1
  19. f(x)=−4x2−3−4x−9
  20. f(x)=3x2+4−3x+8

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

The Quotient RuleAnswer keyVersion 1

Date Period

Differentiate each function.

  1. f(x)=x2+92x+72x2+14x−18(2x+7)2
  2. f(x)=−5x2−5−2x−25x2+10x−52(x+1)2
  3. f(x)=−x2−7−x−4x2+8x−7(x+4)2
  4. f(x)=4x2−23x+212x2+16x+6(3x+2)2
  5. f(x)=3x2+9−4x−3−12x2−18x+36(4x+3)2
  6. f(x)=−2x2−7x−1−2x2+4x+7(x−1)2
  7. f(x)=5x2−92x−710x2−70x+18(2x−7)2
  8. f(x)=5x2+94x−120x2−10x−36(4x−1)2
  9. f(x)=2x2+53x−76x2−28x−15(3x−7)2
  10. f(x)=x2+2−x−3−x2−6x+2(x+3)2
  11. f(x)=3x2+14x−23x2−3x−1(2x−1)2
  12. f(x)=−5x2−23x−2−15x2+20x+6(3x−2)2
  13. f(x)=−x2−7x+5−x2−10x+7(x+5)2
  14. f(x)=−4x2−94x−2−4x2+4x+9(2x−1)2
  15. f(x)=−5x2−7x−8−5x2+80x+7(x−8)2
  16. f(x)=4x2−1−2x+3−8x2+24x−2(2x−3)2
  17. f(x)=2x2+83x−46x2−16x−24(3x−4)2
  18. f(x)=−2x2−9x−1−2x2+4x+9(x−1)2
  19. f(x)=−4x2−3−4x−916x2+72x−12(4x+9)2
  20. f(x)=3x2+4−3x+8−9x2+48x+12(3x−8)2

Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

How to do these

f(x)=x2x+1

  1. Bottom times the top derivative: (x + 1)(2x).
  2. Minus top times the bottom derivative.
  3. All over (x + 1) squared.

The answer is 2x(x+1)−x2(x+1)2.

Where students go wrong

Subtracting the other way round. Swapping those two terms flips the sign of the whole answer, and it is the most common slip on the page.

Also called derivative of a quotient or differentiation quotient rule.

Questions about these worksheets

Yes. Every quotient rule sheet is free to print and free to download as a PDF. There is no account to make, no email to hand over and no limit on how many you take.

Yes. The answer key prints on a second page, and you can choose whether it shows each question beside its answer or just the answers in a list.

Yes. Print straight from the page, or download the PDF and print that. The sheet is laid out for paper rather than squeezed off a screen, so there is room to work under each question, and the answer key comes out on its own page.

Calculus is usually taken around 12th grade or a first college course, though schools vary and plenty of students meet it earlier or later. Pick the difficulty rather than the grade: the easy level suits a first lesson on it, the hard level suits review before a test.

Yes, as many as you like. The questions are built fresh each time rather than picked from a fixed set of files, so pressing Generate gives a new sheet. That is what you want for a second class, a retake, or two students sitting next to each other.

That is the closest comparison, and Kuta Software is good software. It is also paid software you install on a computer. These worksheets run in a browser tab for free, with no account and nothing to install. Like Kuta, the quotient rule questions are generated when you ask for them rather than pulled from a fixed set of files, so two classes never get the same sheet, and the answer key comes with it.

Yes. There are three levels, and you can tick more than one for a sheet that mixes them, in which case the questions come out easiest first. The harder levels are not just larger numbers: they ask for something the easy ones do not.

Subtracting the other way round. Swapping those two terms flips the sign of the whole answer, and it is the most common slip on the page.