Level

Text form:

$$f'(x)=$$

Difficulty level:

 Polynomials, rational functions, power functions, root functions, plus... ex ax ln x loga x sin/cos tan sec/csc/cot inverse sin/cos/tan sinh/cosh tanh sech/csch/coth inverse sinh/cosh/tanh

### How to enter expressions

For the most part, expressions are entered using standard mathematical notation, with a few caveats:

• Multiplication is implied in expressions like:
• 2x(3x^2-1)
• cos(x)sin(x)
• (x+1)(x-2)
• ln(4)4^x
• x|x+1|
• x cos(x) (There must be a space between x and cos.)
• Closing parentheses are not optional (unlike, say, on TI-84 graphing calculators).
• All functions must have parentheses—for example, use sin(x) rather than sin x, and ln(|x|) rather than ln|x|.
• Exponentiation (like 7x) can be entered as either 7^x or power(7,x), and ex can be entered as e^x or exp(x). (Note that e^2x is e2x.)
• The inverse trig functions should be entered as atan, asin, and acos (and similarly for inverse hyperbolic trig). However, some alternate notations are also accepted (for example, arctan).
• Absolute values can be entered as either |x| or abs(x).

### Details, quirks, and additional information

I also have a (very rough) page where you can practice integration (antiderivatives).

While I try to test this page fairly thoroughly, every time I change something, I run the risk of breaking something else. If you find it is misbehaving for you, please click THIS LINK to send me an email report of the problem.

For "skipped" functions, this page provides a link to wolframalpha.com where you can see the details of how to find the derivative (follow the link, then click "Show steps"). Note that this might fail for some functions, because some of my notation is tricky to translate to a form that Wolfram|Alpha will understand. Update: While "show steps" used to be free, it is now only available if you pay for "Wolfram|Alpha Pro."

To check if your answer is correct, the computer finds the exact derivative. If your function and the exact derivative have the same output value at 5 randomly selected x values between –8 and +8, it is judged to be the correct answer.

Because of this approach, a few (mostly) correct derivatives will be judged as wrong unless you enter them the "correct" way. For example, if you simplify the function sqrt(x2) to x, and enter the derivative as 1, it would (most of the time) be ruled incorrect. This is because sqrt(x2) = |x|, and the derivative of |x| is ±1 (specifically, +1 when x>0, and -1 when x<0). If you enter the derivative as abs(x)/x, or as x/sqrt(x^2), it will be counted as correct. I don't know of any other issues, but I have not tested this page to the point that I can guarantee it will never fail.

I created this page a LONG time ago (the oldest backup copy I was able to find was dated 2008) when I discovered (to my surprise) that there seemed to be nothing like it on the Internet.

If all else fails, you can access the old version of this page

#### Condensed release history:

(October 2020) Long-overdue interface updates, including removing the legacy MooTools dependencies (switching over to jQuery). Now uses MathJax instead of my clunky homebrewed solution for "typesetting" formulas.

(2008 or so) First release. Minor changes after that, but nothing substantial for a very long time. (Records of those changes are unreliable, because I was not very diligent at tracking them.)

#### TODO:

• I have a whole email folder full of suggestions from the "fan mail" I have received. At some point, I will summarize it here, and then work my way through implementing them.

The contents of this page are © 2020 Darryl Nester. It is available to anyone who wishes to use it (like most things on the Internet). Please send me an email if you have found it to be useful, or if you have suggestions.