Worked Derivative
Type a function and take the derivative one rule at a time . Each line
names the rule it used, so you can find the exact step where your own work
went a different way.
Try to say which rule comes next before you press the
button — that is the part the answer alone never teaches.
f (x ) =
Write it as you would say it: x^2 e^x, sin(3x^2),
(3x+1)/(x^2-4), sqrt(2x+5), ln(cos(x^3)).
product
quotient
chain
chain twice
root
x^x
Worked Derivative
Type any function of one variable. The page differentiates it the way you
would on paper: one rule per line, with the rule named beside the line that
used it.
Use it to find your mistake, not to avoid the work
The value is in the middle lines. If your answer disagrees with the last
line, walk down from the top until the working stops matching yours — that
line is the one to re-learn, and it is almost never the last one.
Next step reveals one line at a time on purpose. Say which rule
applies before you press it. Getting that right is the skill;
executing the rule is the easy half.
How the lines are written
A derivative that has not been taken yet is left standing as
before either half is evaluated. The last line tidies the algebra, and is
marked Tidy up — no new calculus happens there.
Reading the marks
Each rule is written above the operator it put there: PR over the
+ of a product rule, QR over the − of a quotient rule,
CR over the · of a chain rule. The margin names the rule; the
mark says which part of the line it acted on.
Constants come out first
3x ⁴ is handled by the constant multiple rule and then the
power rule — not by the product rule. The page separates those two steps
because running a numeric coefficient through the product rule is a common
and expensive habit.
What it will not do
The tidy-up is algebraic. It knows sin²u + cos²u = 1 and
nothing else about trig identities, so an answer may be correct and still
not look like the one in the back of the book. To settle that, use
Check My Answer , which compares the
two numerically.
It differentiates with respect to whichever variable appears. If more than
one letter appears, it uses x — or whatever ?var= says —
and treats the rest as constants.
Putting this in a slide or a page
?f=sin(3x^2)&embed=true&steps=all&controls=none
gives the finished working with no function box. Leave steps
off and the class advances it a line at a time. See
docs/url-api.md for every parameter.
Keyboard
N Next step
A Show all the working
? This dialog
Esc Close
Close