Abhirup Bhakta

Derivative of absolute value of x. The derivative of mod x is denoted by d/dx(|x|) and it is equal to x/|x| for all nonzero values of x. In this post, we will learn how to differentiate modulus x.

Recall that mod x is defined as below.

$|x|=\begin{cases} x, & \text{ if } x\geq 0 \\ -x, & \text{ if } x< 0 \end{cases}$

The derivative of |x|, that is, the derivative of modulus x, denoted by d/dx(|x|), is given as follows:

$\dfrac{d}{dx}(|x|)=\dfrac{x}{|x|}$ for $x \neq 0$.

Let us now find the derivative of mod x.

Question: Find $\dfrac{d}{dx}(|x|)$.

Answer:

Case 1: First we assume that x>0.

Thus, by the above definition of |x|, we have |x|=x.

∴ d/dx(|x|) = d/dx(x) = 1

Case 2: First we assume that x<0.

So, again by the above definition of |x|, we have |x|=-x.

In this case, d/dx(|x|) = d/dx(-x) = -1

Thus, we obtain that

$\dfrac{d}{dx}(|x|)=\begin{cases} 1, & \text{ if } x> 0 \\ -1, & \text{ if } x< 0 \end{cases}$

Combining both cases, we get that

$\dfrac{d}{dx}(|x|)=\dfrac{x}{|x|}$ for $x \neq 0$.

NOTE: The function f(x)=|x| is not differentiable. For a proof, CLICK HERE.

Remark:

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edit: This answer works, but nowadays you should just use the requests library as mentioned by other answers below.

Use httplib.

>>> import httplib">>> conn = httplib.HTTPConnection("www.google.com")">>> conn.request("HEAD", "/index.html")">>> res = conn.getresponse()">>> print res.status, res.reason"200 OK">>> print res.getheaders()"[('content-length', '0'), ('expires', '-1'), ('server', 'gws'), ('cache-control', 'private, max-age=0'), ('date', 'Sat, 20 Sep 2008 06:43:36 GMT'), ('content-type', 'text/html; charset=ISO-8859-1')]

There's also a getheader(name) to get a specific header.

If you want a general function which you can pass as a parameter to sort(key=XXX), then here's a candidate complete with test:

DATA = ["    { 'name' : 'A', 'value' : '10.0' },"    { 'name' : 'B', 'value' : '2.0' },"]""def get_attr(name):"    def inner_func(o):"        try:"            rv = float(o[name])"        except ValueError:"            rv = o[name]"        return rv"    return inner_func""for attrname in ('name', 'value'):"    DATA.sort(key=get_attr(attrname))"    print "%r-sorted: %s" % (attrname, DATA)

When you run the above script, you get:

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Either redirect like your example, or use AJAX to submit the form in the first place. The browser has no way of requesting the same page without requesting the same page.

Not re-submitting the data would be the same as requesting a different page, so you're kinda stuck.

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