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The derivative of the function/ arcctg4x-(x/4)

Derivative of arcctg4x-(x/4)

Function f() - derivative -N order at the point
v

The graph:

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Piecewise:

The solution

You have entered [src] 
            x
acot(4*x) - -
            4
$$- \frac{x}{4} + \operatorname{acot}{\left(4 x \right)}$$ 
acot(4*x) - x/4
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  1       4    
- - - ---------
  4           2
      1 + 16*x
$$- \frac{1}{4} - \frac{4}{16 x^{2} + 1}$$
Simplify
The second derivative [src] 
   128*x    
------------
           2
/        2\ 
\1 + 16*x /
$$\frac{128 x}{\left(16 x^{2} + 1\right)^{2}}$$
Simplify
The third derivative [src] 
    /          2  \
    |      64*x   |
128*|1 - ---------|
    |            2|
    \    1 + 16*x /
-------------------
               2   
    /        2\    
    \1 + 16*x /
$$\frac{128 \left(- \frac{64 x^{2}}{16 x^{2} + 1} + 1\right)}{\left(16 x^{2} + 1\right)^{2}}$$
Simplify
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