Worksheets · Calculus

Derivatives of trig functions worksheet

Six to know. Sine goes to cosine, cosine goes to minus sine, and the other four follow from those two. Anything other than a plain x inside brings the chain rule with it.

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Pick more than one for a sheet that mixes them.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Trig Functions

Date Period

Differentiate each function.

  1. f(x)=cos(3x)
  2. f(x)=6tan(3x)
  3. f(x)=4sin(2x)
  4. f(x)=7tan(2x)
  5. f(x)=7sec(2x)
  6. f(x)=2cot(4x)
  7. f(x)=7cos(2x)
  8. f(x)=6sin(3x)
  9. f(x)=7tan(2x)
  10. f(x)=6cot(4x)
  11. f(x)=8cos(2x)
  12. f(x)=5csc(4x)
  13. f(x)=2sin(4x)
  14. f(x)=3sin(3x)
  15. f(x)=7cot(2x)
  16. f(x)=2sin(3x)
  17. f(x)=sin(2x)
  18. f(x)=5cot(2x)
  19. f(x)=3cot(4x)
  20. f(x)=6cos(2x)

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

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Trig FunctionsAnswer keyVersion 1

Date Period

Differentiate each function.

  1. f(x)=cos(3x)3sin(3x)
  2. f(x)=6tan(3x)18sec2(3x)
  3. f(x)=4sin(2x)8cos(2x)
  4. f(x)=7tan(2x)14sec2(2x)
  5. f(x)=7sec(2x)14sec(2x)tan(2x)
  6. f(x)=2cot(4x)8csc2(4x)
  7. f(x)=7cos(2x)14sin(2x)
  8. f(x)=6sin(3x)18cos(3x)
  9. f(x)=7tan(2x)14sec2(2x)
  10. f(x)=6cot(4x)24csc2(4x)
  11. f(x)=8cos(2x)16sin(2x)
  12. f(x)=5csc(4x)20csc(4x)cot(4x)
  13. f(x)=2sin(4x)8cos(4x)
  14. f(x)=3sin(3x)9cos(3x)
  15. f(x)=7cot(2x)14csc2(2x)
  16. f(x)=2sin(3x)6cos(3x)
  17. f(x)=sin(2x)2cos(2x)
  18. f(x)=5cot(2x)10csc2(2x)
  19. f(x)=3cot(4x)12csc2(4x)
  20. f(x)=6cos(2x)12sin(2x)

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

How to do these

f(x)=3sin2x

  1. The derivative of sine is cosine.
  2. The inside is 2x, whose derivative is 2.
  3. Three times two is six.

The answer is 6cos2x.

Where students go wrong

Losing the minus sign on cosine. Half of these ratios differentiate to something negative, and the sheet will keep asking until it catches you.

Also called derivative of sine and cosine, trig derivatives or derivative of tangent.

Questions about these worksheets

Yes. Every derivatives of trig functions 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 derivatives of trig functions 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.

Losing the minus sign on cosine. Half of these ratios differentiate to something negative, and the sheet will keep asking until it catches you.