Nothing here can be differentiated, because there are no formulas. The rules are what turn a few numbers into an answer, which is a good test of whether they are understood or just copied. Where only values of f are given, the slope between nearby points estimates f'.
Select your difficulty
Pick more than one for a sheet that mixes them.
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Find h′(1) where h(x)=f(x)x2−3.xf(x)f′(x)g(x)g′(x)141462−1−14−53−2−584445−4−1
Find h′(1) where h(x)=x2+2g(x).xf(x)f′(x)g(x)g′(x)−2−2−17−3−1−115303−18−210−4−21
Find h′(2) where h(x)=g(x)2x+3.xf(x)f′(x)g(x)g′(x)2821−136−1−2−64−250152252
Find h′(2) where h(x)=x3f(x).xf(x)f′(x)g(x)g′(x)125−4−227−5−143152−241−476
Find h′(3) where h(x)=3x+1f(x).xf(x)f′(x)g(x)g′(x)18−43423−47−23−25454−4−52−2
Find h′(4) where h(x)=g(x)f(x)+5.xf(x)f′(x)g(x)g′(x)285−443−1−1−264−212−255−255
Find h′(2) where h(x)=f(x)x3.xf(x)f′(x)g(x)g′(x)2357−534−1−154355257−67−2
Use the chain rule with the table
Find h′(3) where h(x)=g(f(x)).xf(x)f′(x)g(x)g′(x)1238−52352533−14−155315
Find h′(1) where h(x)=ln(f(x)).xf(x)f′(x)g(x)g′(x)16−40−3254−3234−3225−2−634
Find h′(1) where h(x)=f(2x).xf(x)f′(x)g(x)g′(x)−24−1−33−1−430−111−5−1320544
Find h′(3) where h(x)=f(x).xf(x)f′(x)g(x)g′(x)18−3−432714−439−3−1−641−3−44
Find h′(1) where h(x)=[f(x)]3.xf(x)f′(x)g(x)g′(x)−1−44−3−306−1−3211−2312−365−6
Find h′(2) where h(x)=g(x3).xf(x)f′(x)g(x)g′(x)1−34562−227−34123−581−5−33
Find h′(0) where h(x)=f(x)4.xf(x)f′(x)g(x)g′(x)−2−3−684−1534−10−2−41−5165−2−4
Estimate the derivative from each table
Use the table values on either side of x=4 to estimate f′(4).xf(x)224856839−2
Use the last two values in the table to estimate f′(9).xf(x)19310511714920
The water in a tank, in gallons, t hours after a pump is switched on is W(t).Use the values on either side of t=6 to estimate W′(6).tW(t)057259464668873
Use the values of f on either side of x=6 to estimate h′(6),where h(x)=3f(x)+3x.xf(x)0152124106683
Use the table values on either side of x=2 to estimate f′(2).xf(x)1.8−10.121.9−11.532−132.1−14.532.2−16.12
Use the table values on either side of x=4 to estimate f′(4).xf(x)3−2415−56−117−14
Find h′(1) where h(x)=f(x)x2−3.xf(x)f′(x)g(x)g′(x)141462−1−14−53−2−584445−4−185
Find h′(1) where h(x)=x2+2g(x).xf(x)f′(x)g(x)g′(x)−2−2−17−3−1−115303−18−210−4−2197
Find h′(2) where h(x)=g(x)2x+3.xf(x)f′(x)g(x)g′(x)2821−136−1−2−64−2501522529
Find h′(2) where h(x)=x3f(x).xf(x)f′(x)g(x)g′(x)125−4−227−5−143152−241−476−1631
Find h′(3) where h(x)=3x+1f(x).xf(x)f′(x)g(x)g′(x)18−43423−47−23−25454−4−52−22514
Find h′(4) where h(x)=g(x)f(x)+5.xf(x)f′(x)g(x)g′(x)285−443−1−1−264−212−255−2552
Find h′(2) where h(x)=f(x)x3.xf(x)f′(x)g(x)g′(x)2357−534−1−154355257−67−2−94
Use the chain rule with the table
Find h′(3) where h(x)=g(f(x)).xf(x)f′(x)g(x)g′(x)1238−52352533−14−1553151
Find h′(1) where h(x)=ln(f(x)).xf(x)f′(x)g(x)g′(x)16−40−3254−3234−3225−2−634−32
Find h′(1) where h(x)=f(2x).xf(x)f′(x)g(x)g′(x)−24−1−33−1−430−111−5−132054410
Find h′(3) where h(x)=f(x).xf(x)f′(x)g(x)g′(x)18−3−432714−439−3−1−641−3−44−21
Find h′(1) where h(x)=[f(x)]3.xf(x)f′(x)g(x)g′(x)−1−44−3−306−1−3211−2312−365−6−6
Find h′(2) where h(x)=g(x3).xf(x)f′(x)g(x)g′(x)1−34562−227−34123−581−5−3336
Find h′(0) where h(x)=f(x)4.xf(x)f′(x)g(x)g′(x)−2−3−684−1534−10−2−41−5165−2−44
Estimate the derivative from each table
Use the table values on either side of x=4 to estimate f′(4).xf(x)224856839−234
Use the last two values in the table to estimate f′(9).xf(x)193105117149203
The water in a tank, in gallons, t hours after a pump is switched on is W(t).Use the values on either side of t=6 to estimate W′(6).tW(t)0572594646688732.25 gallons per hour
Use the values of f on either side of x=6 to estimate h′(6),where h(x)=3f(x)+3x.xf(x)0152124106683−2.25
Use the table values on either side of x=2 to estimate f′(2).xf(x)1.8−10.121.9−11.532−132.1−14.532.2−16.12−15
Use the table values on either side of x=4 to estimate f′(4).xf(x)3−2415−56−117−14−1.5
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 (easy), the quotient rule (medium), the product or quotient rule with the chain rule (hard)
Find h′(2) where h(x)=3f(x)−2g(x)+x3.xf(x)f′(x)g(x)g′(x)12−42−12542135−5−4−2572−16→ 22
The product rule (easy), the chain rule (medium), compositions in two layers or with a nonlinear inside (hard)
Find h′(3) where h(x)=(x2+4)g(x).xf(x)f′(x)g(x)g′(x)11−64−52−3−1−3−23−24065−2−334→ 78
Sums with products (easy), estimating the derivative from data (medium), tangent lines from the table (hard)
Find h′(1) where h(x)=f(x)g(x)−xf(x).xf(x)f′(x)g(x)g′(x)−1530−503−1131036−3231−1−1→ 15
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 3: sums and multiples (easy), the quotient rule (medium), the product or quotient rule with the chain rule (hard), the product rule (easy), the chain rule (medium), compositions in two layers or with a nonlinear inside (hard) and sums with products (easy), estimating the derivative from data (medium), tangent lines from the table (hard). 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.