Derivatives of logarithmic functions worksheet

A natural log gives one over the inside, and the chain rule puts the inside derivative on top. Any other base divides the whole thing by the natural log of that base.

Select your difficulty

Pick more than one for a sheet that mixes them.



Sigma Prep · sigmaprep.io/worksheets Name Derivatives of Logarithmic Functions Date Period Differentiate each function. $f (x) = \ln (4 x - 4)$ $f (x) = 4 \ln (5 x - 6)$ $f (x) = - 2 \log_{2} (3 x + 5)$ $f (x) = - 4 \ln (4 x - 5)$ $f (x) = 7 \ln (2 x + 5)$ $f (x) = - 7 \log_{5} (2 x - 4)$ $f (x) = 2 \log_{10} (3 x + 6)$ $f (x) = 4 \ln (3 x + 7)$ $f (x) = 8 \log_{10} (5 x + 6)$ $f (x) = 9 \log_{10} (4 x + 8)$ $f (x) = - 4 \ln (2 x + 3)$ $f (x) = \log_{10} (5 x - 6)$ $f (x) = - 2 \log_{2} (4 x - 6)$ $f (x) = - 7 \log_{10} (4 x + 1)$ $f (x) = - 9 \log_{10} (5 x - 5)$ $f (x) = - 7 \ln (5 x + 6)$ $f (x) = 2 \log_{10} (2 x + 1)$ $f (x) = - 9 \log_{3} (5 x - 5)$ $f (x) = - 3 \log_{2} (5 x - 3)$ $f (x) = 4 \ln (2 x - 3)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Logarithmic Functions

Date Period

Differentiate each function.

$f (x) = \ln (4 x - 4)$
$f (x) = 4 \ln (5 x - 6)$
$f (x) = - 2 \log_{2} (3 x + 5)$
$f (x) = - 4 \ln (4 x - 5)$
$f (x) = 7 \ln (2 x + 5)$
$f (x) = - 7 \log_{5} (2 x - 4)$
$f (x) = 2 \log_{10} (3 x + 6)$
$f (x) = 4 \ln (3 x + 7)$
$f (x) = 8 \log_{10} (5 x + 6)$
$f (x) = 9 \log_{10} (4 x + 8)$
$f (x) = - 4 \ln (2 x + 3)$
$f (x) = \log_{10} (5 x - 6)$
$f (x) = - 2 \log_{2} (4 x - 6)$
$f (x) = - 7 \log_{10} (4 x + 1)$
$f (x) = - 9 \log_{10} (5 x - 5)$
$f (x) = - 7 \ln (5 x + 6)$
$f (x) = 2 \log_{10} (2 x + 1)$
$f (x) = - 9 \log_{3} (5 x - 5)$
$f (x) = - 3 \log_{2} (5 x - 3)$
$f (x) = 4 \ln (2 x - 3)$



Sigma Prep · sigmaprep.io/worksheets Name Derivatives of Logarithmic FunctionsAnswer keyVersion 1 Date Period Differentiate each function. $f (x) = \ln (4 x - 4)$ $\frac{1}{x - 1}$ $f (x) = 4 \ln (5 x - 6)$ $\frac{20}{5 x - 6}$ $f (x) = - 2 \log_{2} (3 x + 5)$ $- \frac{6}{(3 x + 5) \ln 2}$ $f (x) = - 4 \ln (4 x - 5)$ $\frac{- 16}{4 x - 5}$ $f (x) = 7 \ln (2 x + 5)$ $\frac{14}{2 x + 5}$ $f (x) = - 7 \log_{5} (2 x - 4)$ $- \frac{14}{(2 x - 4) \ln 5}$ $f (x) = 2 \log_{10} (3 x + 6)$ $\frac{6}{(3 x + 6) \ln 10}$ $f (x) = 4 \ln (3 x + 7)$ $\frac{12}{3 x + 7}$ $f (x) = 8 \log_{10} (5 x + 6)$ $\frac{40}{(5 x + 6) \ln 10}$ $f (x) = 9 \log_{10} (4 x + 8)$ $\frac{36}{(4 x + 8) \ln 10}$ $f (x) = - 4 \ln (2 x + 3)$ $\frac{- 8}{2 x + 3}$ $f (x) = \log_{10} (5 x - 6)$ $\frac{5}{(5 x - 6) \ln 10}$ $f (x) = - 2 \log_{2} (4 x - 6)$ $- \frac{8}{(4 x - 6) \ln 2}$ $f (x) = - 7 \log_{10} (4 x + 1)$ $- \frac{28}{(4 x + 1) \ln 10}$ $f (x) = - 9 \log_{10} (5 x - 5)$ $- \frac{45}{(5 x - 5) \ln 10}$ $f (x) = - 7 \ln (5 x + 6)$ $\frac{- 35}{5 x + 6}$ $f (x) = 2 \log_{10} (2 x + 1)$ $\frac{4}{(2 x + 1) \ln 10}$ $f (x) = - 9 \log_{3} (5 x - 5)$ $- \frac{45}{(5 x - 5) \ln 3}$ $f (x) = - 3 \log_{2} (5 x - 3)$ $- \frac{15}{(5 x - 3) \ln 2}$ $f (x) = 4 \ln (2 x - 3)$ $\frac{8}{2 x - 3}$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Logarithmic FunctionsAnswer keyVersion 1

Date Period

Differentiate each function.

$f (x) = \ln (4 x - 4)$ $\frac{1}{x - 1}$
$f (x) = 4 \ln (5 x - 6)$ $\frac{20}{5 x - 6}$
$f (x) = - 2 \log_{2} (3 x + 5)$ $- \frac{6}{(3 x + 5) \ln 2}$
$f (x) = - 4 \ln (4 x - 5)$ $\frac{- 16}{4 x - 5}$
$f (x) = 7 \ln (2 x + 5)$ $\frac{14}{2 x + 5}$
$f (x) = - 7 \log_{5} (2 x - 4)$ $- \frac{14}{(2 x - 4) \ln 5}$
$f (x) = 2 \log_{10} (3 x + 6)$ $\frac{6}{(3 x + 6) \ln 10}$
$f (x) = 4 \ln (3 x + 7)$ $\frac{12}{3 x + 7}$
$f (x) = 8 \log_{10} (5 x + 6)$ $\frac{40}{(5 x + 6) \ln 10}$
$f (x) = 9 \log_{10} (4 x + 8)$ $\frac{36}{(4 x + 8) \ln 10}$
$f (x) = - 4 \ln (2 x + 3)$ $\frac{- 8}{2 x + 3}$
$f (x) = \log_{10} (5 x - 6)$ $\frac{5}{(5 x - 6) \ln 10}$
$f (x) = - 2 \log_{2} (4 x - 6)$ $- \frac{8}{(4 x - 6) \ln 2}$
$f (x) = - 7 \log_{10} (4 x + 1)$ $- \frac{28}{(4 x + 1) \ln 10}$
$f (x) = - 9 \log_{10} (5 x - 5)$ $- \frac{45}{(5 x - 5) \ln 10}$
$f (x) = - 7 \ln (5 x + 6)$ $\frac{- 35}{5 x + 6}$
$f (x) = 2 \log_{10} (2 x + 1)$ $\frac{4}{(2 x + 1) \ln 10}$
$f (x) = - 9 \log_{3} (5 x - 5)$ $- \frac{45}{(5 x - 5) \ln 3}$
$f (x) = - 3 \log_{2} (5 x - 3)$ $- \frac{15}{(5 x - 3) \ln 2}$
$f (x) = 4 \ln (2 x - 3)$ $\frac{8}{2 x - 3}$

How to do these

$f (x) = \ln (5 x + 2)$

The derivative of a natural log is one over the inside.
The chain rule puts the inside derivative on top, and that is 5.
So it is 5 over 5x plus 2.

The answer is $\frac{5}{5 x + 2}$ .

Where students go wrong

Forgetting what the inside contributes. The derivative of ln of a bracket is not one over the bracket on its own: whatever the bracket differentiates to goes on top.

Also called derivative of ln x, logarithmic derivatives, derivative of log x or differentiating logarithms.

Questions about these worksheets

Yes. Every derivatives of logarithmic 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 logarithmic 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.

Forgetting what the inside contributes. The derivative of ln of a bracket is not one over the bracket on its own: whatever the bracket differentiates to goes on top.

Derivatives of logarithmic functions worksheet

Select your difficulty

Derivatives of Logarithmic Functions

Derivatives of Logarithmic FunctionsAnswer keyVersion 1

How to do these

Where students go wrong

Questions about these worksheets

Are these derivatives of logarithmic functions worksheets free?+

Do the derivatives of logarithmic functions worksheets come with an answer key?+

Are these derivatives of logarithmic functions worksheets printable?+

What grade are these derivatives of logarithmic functions worksheets for?+

Can I get a different version of the same derivatives of logarithmic functions worksheet?+

Is this a free alternative to Kuta Software for derivatives of logarithmic functions?+

Can I choose how hard the derivatives of logarithmic functions questions are?+

What do students get wrong with derivatives of logarithmic functions?+