Worksheets · Calculus

Derivatives of exponential functions worksheet

e to the x is its own derivative, which is the whole reason it is the base everyone uses. Any other base keeps its shape too, but picks up a natural log as a multiplier.

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

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Exponential Functions

Date Period

Differentiate each function.

  1. Differentiate exponential functions

    f(x)=e4x
  2. f(x)=−3e2x
  3. f(x)=−7⋅35x
  4. f(x)=4e3x
  5. f(x)=2⋅104x
  6. f(x)=33x
  7. f(x)=3⋅22x
  8. f(x)=−7e5x
  9. f(x)=−25x
  10. f(x)=−3⋅102x

  1. Differentiate quotients with exponentials

    Find f′(x) for f(x)=exx2
  2. Find f′(x) for f(x)=xe5x
  3. Find f′(x) for f(x)=ex−9ex
  4. Find f′(x) for f(x)=11+e4x
  5. Find f′(x) for f(x)=e3xx2
  6. Find f′(x) for f(x)=xex
  7. Find f′(x) for f(x)=e6xx
  8. Find f′(x) for f(x)=exx
  9. Find f′(x) for f(x)=11+ex
  10. Find f′(x) for f(x)=11+e3x

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

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Exponential FunctionsAnswer keyVersion 1

Date Period

Differentiate each function.

  1. Differentiate exponential functions

    f(x)=e4xf′(x)=4e4x
  2. f(x)=−3e2xf′(x)=−6e2x
  3. f(x)=−7⋅35xf′(x)=−35⋅35xln⁡3
  4. f(x)=4e3xf′(x)=12e3x
  5. f(x)=2⋅104xf′(x)=8⋅104xln⁡10
  6. f(x)=33xf′(x)=3⋅33xln⁡3
  7. f(x)=3⋅22xf′(x)=6⋅22xln⁡2
  8. f(x)=−7e5xf′(x)=−35e5x
  9. f(x)=−25xf′(x)=−5⋅25xln⁡2
  10. f(x)=−3⋅102xf′(x)=−6⋅102xln⁡10

  1. Differentiate quotients with exponentials

    Find f′(x) for f(x)=exx2f′(x)=ex(x−2)x3
  2. Find f′(x) for f(x)=xe5xf′(x)=1−5xe5x
  3. Find f′(x) for f(x)=ex−9exf′(x)=9e−x
  4. Find f′(x) for f(x)=11+e4xf′(x)=−4e4x(1+e4x)2
  5. Find f′(x) for f(x)=e3xx2f′(x)=e3x(3x−2)x3
  6. Find f′(x) for f(x)=xexf′(x)=1−xex
  7. Find f′(x) for f(x)=e6xxf′(x)=e6x(6x−1)x2
  8. Find f′(x) for f(x)=exxf′(x)=ex(x−1)x2
  9. Find f′(x) for f(x)=11+exf′(x)=−ex(1+ex)2
  10. Find f′(x) for f(x)=11+e3xf′(x)=−3e3x(1+e3x)2

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

How to do these

f(x)=4e3x

  1. An exponential differentiates to itself.
  2. The chain rule brings the 3 out in front.
  3. So it is 12 e to the 3x.

The answer is f′(x)=12e3x.

Where students go wrong

Treating a base other than e like e. Two to the x differentiates to itself times ln 2, and that extra factor is only ever 1 when the base is e.

Also called derivative of e^x, exponential derivatives, derivative of 2^x or differentiating exponentials.

What you can put on this worksheet

Derivatives of exponentials
f(x)=6e−x → f′(x)=−6e−x
Quotients of exponentials
Find f′(x) for f(x)=e4xx → f′(x)=e4x(4x−1)x2

Questions about these worksheets

Yes. Every derivatives of exponential 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 exponential 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.

You pick from 2: derivatives of exponentials and quotients of exponentials. Tick as many as you want and set how many of each, or let it spread them evenly.

Treating a base other than e like e. Two to the x differentiates to itself times ln 2, and that extra factor is only ever 1 when the base is e.