Derivative of arctg1/x

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atan(1)
-------
   x

$$\frac{\operatorname{atan}{\left(1 \right)}}{x}$$

atan(1)/x

Detail solution

The derivative of a constant times a function is the constant times the derivative of the function.
1. Apply the power rule: $\frac{1}{x}$ goes to $- \frac{1}{x^{2}}$
So, the result is: $- \frac{\operatorname{atan}{\left(1 \right)}}{x^{2}}$
Now simplify:

$- \frac{\pi}{4 x^{2}}$

The answer is:

$- \frac{\pi}{4 x^{2}}$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

-atan(1) 
---------
     2   
    x

$$- \frac{\operatorname{atan}{\left(1 \right)}}{x^{2}}$$

Simplify

The second derivative [src]

2*atan(1)
---------
     3   
    x

$$\frac{2 \operatorname{atan}{\left(1 \right)}}{x^{3}}$$

Simplify

The third derivative [src]

-6*atan(1)
----------
     4    
    x

$$- \frac{6 \operatorname{atan}{\left(1 \right)}}{x^{4}}$$

Simplify

The graph