Reflecting a graph in the line y = x turns a slope into its reciprocal, so the derivative of the inverse at a point is one over the derivative of the original at the matching point. The inverse itself never has to be written down.
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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.
Find what f sends to 4: f of 1 is 1 plus 2 plus 1, which is 4.
The derivative is 3x squared plus 2, which is 5 at x equals 1.
So the answer is one fifth.
The answer is 51.
Where students go wrong
Using the derivative at the wrong point. It is read at the x that maps to the value asked about, not at the value itself, and those are only the same by accident.
Also called inverse function theorem, f inverse prime or reciprocal of the derivative.
What you can put on this worksheet
Derivative of an inverse function
If f(x)=5x+1,find (f−1)′(11)→ 51
From a table of values
f is one-to-oneand g=f−1.Find g′(−5).xf(x)f′(x)1−1−32−4−33−5−44−7−2→ −41
Non-polynomial functions
f(x)=x3+2x+1.Find (f−1)′(4)→ 51
The inverse's derivative as a formula
Find (f−1)′(x)for f(x)=ex+1→ (f−1)′(x)=x−11,x>1
Questions about these worksheets
Yes. Every derivative of an inverse function 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 derivative of an inverse function 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 4: derivative of an inverse function, from a table of values, non-polynomial functions and the inverse's derivative as a formula. Tick as many as you want and set how many of each, or let it spread them evenly.
Using the derivative at the wrong point. It is read at the x that maps to the value asked about, not at the value itself, and those are only the same by accident.