Are these equal?

1. Aug 8, 2011

dimension10

According to Wolfram|Alpha, sometimes, the derivative of arctangent is

$$\frac{d}{dx}\arctan x =\frac{1}{1+{x}^{2}}$$

and sometimes,

$$\frac{d}{dx}\arctan x =\frac{\arctan x}{x}$$

So are both of them equal?

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2. Aug 8, 2011

asmani

The second case is actually
$$\frac{d}{d\times x}\arctan (x)=\frac{\arctan (x)}{x}$$.

3. Aug 8, 2011

HallsofIvy

Staff Emeritus
Okay, you have lost me. What does
$$\frac{d}{d\times x}$$
mean?

4. Aug 8, 2011

asmani

d over d multiplied by x, where d is a constant. Wolframalpha simplifies this to 1/x.

5. Aug 9, 2011

dimension10

Oh. So that must have happened the other time too...

6. Aug 9, 2011

asmani

Compare:

Notice the blank between d and x in the left one.
What input did you give in each time?

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7. Aug 9, 2011

HallsofIvy

Staff Emeritus
Thanks.