Worksheets · Calculus

Power rule worksheet

Bring the exponent down in front and take one off it. A constant on its own disappears, because a flat line has no slope.

Select your difficulty

Pick more than one for a sheet that mixes them.

The preview can look cramped on a phone. The PDF and printed sheet come out normal.

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Power Rule

Date Period

Differentiate each function, or answer as asked.

  1. Differentiate each function

    f(x)=xa+1+9x2
  2. f(x)=10x25
  3. f(x)=9x−23+8
  4. f(x)=ax3−9x+b
  5. f(x)=5x2+3x13−4x−2
  6. f(x)=9x43+3x−23
  7. f(x)=ax−3−7x3

  1. Rewrite each root and fraction as a power of xx, then differentiate

    f(x)=7x−9x3
  2. f(x)=6x3−3
  3. f(x)=4x2+10x
  4. f(x)=10x−3x2
  5. f(x)=−4x4+4x3
  6. f(x)=12x+5x
  7. f(x)=−8x+8

  1. Find the value of the derivative asked for

    f(x)=−6x3−x2. Find f′(8).
  2. f(x)=8x+5x. Find f′(−1).
  3. f(x)=6x3−2. Find f′(1).
  4. f(x)=6x. Find f′(9).
  5. f(x)=−9x+x. Find f′(25).
  6. f(x)=6x−6x. Find f′(4).

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

Sigma Prep · sigmaprep.io/worksheets

Name

The Power RuleAnswer keyVersion 1

Date Period

Differentiate each function, or answer as asked.

  1. Differentiate each function

    f(x)=xa+1+9x2f′(x)=(a+1)xa+18x
  2. f(x)=10x25f′(x)=4x−35
  3. f(x)=9x−23+8f′(x)=−6x−53
  4. f(x)=ax3−9x+bf′(x)=3ax2−9
  5. f(x)=5x2+3x13−4x−2f′(x)=10x+x−23+8x−3
  6. f(x)=9x43+3x−23f′(x)=12x13−2x−53
  7. f(x)=ax−3−7x3f′(x)=−3ax−4−21x2

  1. Rewrite each root and fraction as a power of xx, then differentiate

    f(x)=7x−9x3f′(x)=−7x2+27x4
  2. f(x)=6x3−3f′(x)=−2x43
  3. f(x)=4x2+10xf′(x)=8x+5x
  4. f(x)=10x−3x2f′(x)=−5x3+6x3
  5. f(x)=−4x4+4x3f′(x)=12x2+16x5
  6. f(x)=12x+5xf′(x)=5−14x3
  7. f(x)=−8x+8f′(x)=−4x

  1. Find the value of the derivative asked for

    f(x)=−6x3−x2. Find f′(8).−332
  2. f(x)=8x+5x. Find f′(−1).−3
  3. f(x)=6x3−2. Find f′(1).−2
  4. f(x)=6x. Find f′(9).−19
  5. f(x)=−9x+x. Find f′(25).110
  6. f(x)=6x−6x. Find f′(4).−158

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

How to do these

f(x)=4x3−7x+5

  1. Three times four is twelve, and the power drops to 2.
  2. The x term differentiates to -7.
  3. The 5 is a constant, so it goes.

The answer is f′(x)=12x2−7.

Where students go wrong

Leaving the constant in. It is the one term whose derivative is zero, and it is the one every sheet puts in to see whether you noticed.

Also called differentiation power rule, basic derivatives, constant and sum rules or derivatives of polynomials.

What you can put on this worksheet

Differentiate with the power rule
f(x)=−5x6+3x4+4 → f′(x)=−30x5+12x3
Rewrite as powers of x, then differentiate
f(x)=(2x)3+x2 → f′(x)=24x2+2x
The derivative at a point
f(x)=−2x9+4x5. Find f′(1). → 2

Questions about these worksheets

Yes. Every power 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 power 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.

You pick from 3: differentiate with the power rule, rewrite as powers of x, then differentiate and the derivative at a point. Tick as many as you want and set how many of each, or let it spread them evenly.

Leaving the constant in. It is the one term whose derivative is zero, and it is the one every sheet puts in to see whether you noticed.