Derivatives of hyperbolic functions worksheet

The hyperbolic derivatives look like the trig ones with fewer minus signs: sinh goes to cosh and cosh goes to sinh, with no sign change at all. tanh goes to sech squared, and the three reciprocals each pick up a minus.

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.



Sigma Prep · sigmaprep.io/worksheets Name Derivatives of Hyperbolic Functions Date Period Differentiate each function. Find $f^{'} (x)$ for $f (x) = \cosh (e^{x})$ Find $f^{'} (x)$ for $f (x) = x^{2} \tanh (2 x)$ Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (x^{4})$ Find $f^{'} (x)$ for $f (x) = sech (3 x)$ Find $f^{'} (x)$ for $f (x) = e^{x} \sinh (2 x)$ Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (4 x)$ Find $f^{'} (x)$ for $f (x) = csch (5 x)$ Find $f^{'} (x)$ for $f (x) = e^{3 x} \cosh (4 x)$ Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (3 x^{4})$ Find $f^{'} (x)$ for $f (x) = \sinh (x^{2} + 2)$ Find $f^{'} (x)$ for $f (x) = e^{x} \cosh (2 x)$ Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (x + 4)$ Find $f^{'} (x)$ for $f (x) = \cosh^{4} (2 x)$ Find $f^{'} (x)$ for $f (x) = e^{5 x} \sinh (5 x)$ Find $f^{'} (x)$ for $f (x) = \tanh^{- 1} (x^{3})$ Find $f^{'} (x)$ for $f (x) = \tanh (x^{2} + 1)$ Find $f^{'} (x)$ for $f (x) = x^{2} \tanh x$ Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (6 x)$ Find $f^{'} (x)$ for $f (x) = \sinh (e^{x})$ Find $f^{'} (x)$ for $f (x) = e^{2 x} \cosh x$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Hyperbolic Functions

Date Period

Differentiate each function.

Find $f^{'} (x)$ for $f (x) = \cosh (e^{x})$
Find $f^{'} (x)$ for $f (x) = x^{2} \tanh (2 x)$
Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (x^{4})$
Find $f^{'} (x)$ for $f (x) = sech (3 x)$
Find $f^{'} (x)$ for $f (x) = e^{x} \sinh (2 x)$
Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (4 x)$
Find $f^{'} (x)$ for $f (x) = csch (5 x)$
Find $f^{'} (x)$ for $f (x) = e^{3 x} \cosh (4 x)$
Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (3 x^{4})$
Find $f^{'} (x)$ for $f (x) = \sinh (x^{2} + 2)$
Find $f^{'} (x)$ for $f (x) = e^{x} \cosh (2 x)$
Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (x + 4)$
Find $f^{'} (x)$ for $f (x) = \cosh^{4} (2 x)$
Find $f^{'} (x)$ for $f (x) = e^{5 x} \sinh (5 x)$
Find $f^{'} (x)$ for $f (x) = \tanh^{- 1} (x^{3})$
Find $f^{'} (x)$ for $f (x) = \tanh (x^{2} + 1)$
Find $f^{'} (x)$ for $f (x) = x^{2} \tanh x$
Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (6 x)$
Find $f^{'} (x)$ for $f (x) = \sinh (e^{x})$
Find $f^{'} (x)$ for $f (x) = e^{2 x} \cosh x$



Sigma Prep · sigmaprep.io/worksheets Name Derivatives of Hyperbolic FunctionsAnswer keyVersion 1 Date Period Differentiate each function. Find $f^{'} (x)$ for $f (x) = \cosh (e^{x})$ $e^{x} \sinh (e^{x})$ Find $f^{'} (x)$ for $f (x) = x^{2} \tanh (2 x)$ $2 x \tanh (2 x) + 2 x^{2} {sech}^{2} (2 x)$ Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (x^{4})$ $\frac{4 x^{3}}{\sqrt{x^{8} + 1}}$ Find $f^{'} (x)$ for $f (x) = sech (3 x)$ $- 3 sech (3 x) \tanh (3 x)$ Find $f^{'} (x)$ for $f (x) = e^{x} \sinh (2 x)$ $e^{x} (\sinh (2 x) + 2 \cosh (2 x))$ Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (4 x)$ $\frac{4}{\sqrt{16 x^{2} - 1}}$ Find $f^{'} (x)$ for $f (x) = csch (5 x)$ $- 5 csch (5 x) \coth (5 x)$ Find $f^{'} (x)$ for $f (x) = e^{3 x} \cosh (4 x)$ $e^{3 x} (3 \cosh (4 x) + 4 \sinh (4 x))$ Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (3 x^{4})$ $\frac{12 x^{3}}{\sqrt{9 x^{8} + 1}}$ Find $f^{'} (x)$ for $f (x) = \sinh (x^{2} + 2)$ $2 x \cosh (x^{2} + 2)$ Find $f^{'} (x)$ for $f (x) = e^{x} \cosh (2 x)$ $e^{x} (\cosh (2 x) + 2 \sinh (2 x))$ Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (x + 4)$ $\frac{1}{\sqrt{{(x + 4)}^{2} - 1}}$ Find $f^{'} (x)$ for $f (x) = \cosh^{4} (2 x)$ $8 \cosh^{3} (2 x) \sinh (2 x)$ Find $f^{'} (x)$ for $f (x) = e^{5 x} \sinh (5 x)$ $e^{5 x} (5 \sinh (5 x) + 5 \cosh (5 x))$ Find $f^{'} (x)$ for $f (x) = \tanh^{- 1} (x^{3})$ $\frac{3 x^{2}}{1 - x^{6}}$ Find $f^{'} (x)$ for $f (x) = \tanh (x^{2} + 1)$ $2 x {sech}^{2} (x^{2} + 1)$ Find $f^{'} (x)$ for $f (x) = x^{2} \tanh x$ $2 x \tanh x + x^{2} {sech}^{2} x$ Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (6 x)$ $\frac{6}{\sqrt{36 x^{2} - 1}}$ Find $f^{'} (x)$ for $f (x) = \sinh (e^{x})$ $e^{x} \cosh (e^{x})$ Find $f^{'} (x)$ for $f (x) = e^{2 x} \cosh x$ $e^{2 x} (2 \cosh x + \sinh x)$ Free math worksheets at sigmaprep.io/worksheets© 2026 Sigma Prep

Sigma Prep · sigmaprep.io/worksheets

Name

Derivatives of Hyperbolic FunctionsAnswer keyVersion 1

Date Period

Differentiate each function.

Find $f^{'} (x)$ for $f (x) = \cosh (e^{x})$ $e^{x} \sinh (e^{x})$
Find $f^{'} (x)$ for $f (x) = x^{2} \tanh (2 x)$ $2 x \tanh (2 x) + 2 x^{2} {sech}^{2} (2 x)$
Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (x^{4})$ $\frac{4 x^{3}}{\sqrt{x^{8} + 1}}$
Find $f^{'} (x)$ for $f (x) = sech (3 x)$ $- 3 sech (3 x) \tanh (3 x)$
Find $f^{'} (x)$ for $f (x) = e^{x} \sinh (2 x)$ $e^{x} (\sinh (2 x) + 2 \cosh (2 x))$
Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (4 x)$ $\frac{4}{\sqrt{16 x^{2} - 1}}$
Find $f^{'} (x)$ for $f (x) = csch (5 x)$ $- 5 csch (5 x) \coth (5 x)$
Find $f^{'} (x)$ for $f (x) = e^{3 x} \cosh (4 x)$ $e^{3 x} (3 \cosh (4 x) + 4 \sinh (4 x))$
Find $f^{'} (x)$ for $f (x) = \sinh^{- 1} (3 x^{4})$ $\frac{12 x^{3}}{\sqrt{9 x^{8} + 1}}$
Find $f^{'} (x)$ for $f (x) = \sinh (x^{2} + 2)$ $2 x \cosh (x^{2} + 2)$
Find $f^{'} (x)$ for $f (x) = e^{x} \cosh (2 x)$ $e^{x} (\cosh (2 x) + 2 \sinh (2 x))$
Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (x + 4)$ $\frac{1}{\sqrt{{(x + 4)}^{2} - 1}}$
Find $f^{'} (x)$ for $f (x) = \cosh^{4} (2 x)$ $8 \cosh^{3} (2 x) \sinh (2 x)$
Find $f^{'} (x)$ for $f (x) = e^{5 x} \sinh (5 x)$ $e^{5 x} (5 \sinh (5 x) + 5 \cosh (5 x))$
Find $f^{'} (x)$ for $f (x) = \tanh^{- 1} (x^{3})$ $\frac{3 x^{2}}{1 - x^{6}}$
Find $f^{'} (x)$ for $f (x) = \tanh (x^{2} + 1)$ $2 x {sech}^{2} (x^{2} + 1)$
Find $f^{'} (x)$ for $f (x) = x^{2} \tanh x$ $2 x \tanh x + x^{2} {sech}^{2} x$
Find $f^{'} (x)$ for $f (x) = \cosh^{- 1} (6 x)$ $\frac{6}{\sqrt{36 x^{2} - 1}}$
Find $f^{'} (x)$ for $f (x) = \sinh (e^{x})$ $e^{x} \cosh (e^{x})$
Find $f^{'} (x)$ for $f (x) = e^{2 x} \cosh x$ $e^{2 x} (2 \cosh x + \sinh x)$

How to do these

Find $f^{'} (x)$ for $f (x) = \cosh (x^{2} + 1)$

The outside is cosh, whose derivative is sinh.
The inside is x^2 + 1, whose derivative is 2x.
f'(x) = 2x sinh(x^2 + 1).

The answer is $2 x \sinh (x^{2} + 1)$ .

Where students go wrong

Bringing a minus over from trig. The derivative of cos x is -sin x, but the derivative of cosh x is +sinh x.

Also called hyperbolic derivatives, derivative of sinh, derivative of cosh or inverse hyperbolic derivatives.

What you can put on this worksheet

The six hyperbolic functions, with the chain rule: Find $f^{'} (x)$ for $f (x) = 3 \tanh (4 x)$ → $12 {sech}^{2} (4 x)$
Products and quotients: Find $f^{'} (x)$ for $f (x) = 3 x \cosh (3 x)$ → $3 \cosh (3 x) + 9 x \sinh (3 x)$
Inverse hyperbolic functions: Find $f^{'} (x)$ for $f (x) = \tanh^{- 1} (6 x)$ → $\frac{6}{1 - 36 x^{2}}$

Questions about these worksheets

Yes. Every derivatives of hyperbolic 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 hyperbolic 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 3: the six hyperbolic functions, with the chain rule, products and quotients and inverse hyperbolic functions. Tick as many as you want and set how many of each, or let it spread them evenly.

Bringing a minus over from trig. The derivative of cos x is -sin x, but the derivative of cosh x is +sinh x.

Derivatives of hyperbolic functions worksheet

Select your difficulty

Derivatives of Hyperbolic Functions

Derivatives of Hyperbolic FunctionsAnswer keyVersion 1

How to do these

Where students go wrong

What you can put on this worksheet

Questions about these worksheets

Are these derivatives of hyperbolic functions worksheets free?+

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

Are these derivatives of hyperbolic functions worksheets printable?+

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

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

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

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

What kinds of question are on a derivatives of hyperbolic functions worksheet?+

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