Nothing here can be differentiated, because there are no formulas. The rules are what turn four numbers into an answer, which is a good test of whether they are understood or just copied.
Given f(2)=3, f′(2)=4, g(2)=5, g′(2)=6, find (fg)′(2)
The product rule is f prime g plus f g prime.
That is 4 times 5, plus 3 times 6.
So it is 20 plus 18, which is 38.
The answer is 38.
Where students go wrong
Reading the chain rule off the wrong row. For f of g of x the outer derivative is read at g of the point, not at the point, and those are two different columns of the table.
Also called derivative rules from a table, product rule from a table, chain rule from a table or table of values derivative.
What you can put on this worksheet
Sums and multiples
Use the table to find h′(3) where h(x)=f(x)+g(x).xf(x)f′(x)g(x)g′(x)12−71−522−62−534723→ 10
The product rule
Use the table to find h′(3) where h(x)=f(x)g(x).xf(x)f′(x)g(x)g′(x)12−71−522−62−534723→ 26
The quotient rule
Use the table to find h′(3) where h(x)=g(x)f(x).xf(x)f′(x)g(x)g′(x)12−71−522−62−534723→ 21
The chain rule
Use the table to find h′(3) where h(x)=f(g(x)).xf(x)f′(x)g(x)g′(x)12−71−522−62−534723→ −18
Questions about these worksheets
Yes. Every derivatives from a table 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 from a table 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: sums and multiples, the product rule, the quotient rule and the chain rule. Tick as many as you want and set how many of each, or let it spread them evenly.
Reading the chain rule off the wrong row. For f of g of x the outer derivative is read at g of the point, not at the point, and those are two different columns of the table.