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The derivative of the function/ arctg((lnx+2)^2)

Derivative of arctg((lnx+2)^2)

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

The graph:

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The solution

You have entered [src] 
    /            2\
atan\(log(x) + 2) /
$$\operatorname{atan}{\left(\left(\log{\left(x \right)} + 2\right)^{2} \right)}$$ 
atan((log(x) + 2)^2)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
    2*(log(x) + 2)   
---------------------
  /                4\
x*\1 + (log(x) + 2) /
$$\frac{2 \left(\log{\left(x \right)} + 2\right)}{x \left(\left(\log{\left(x \right)} + 2\right)^{4} + 1\right)}$$
Simplify
The second derivative [src] 
  /                             4 \
  |               4*(2 + log(x))  |
2*|-1 - log(x) - -----------------|
  |                              4|
  \              1 + (2 + log(x)) /
-----------------------------------
        2 /                4\      
       x *\1 + (2 + log(x)) /
$$\frac{2 \left(- \log{\left(x \right)} - 1 - \frac{4 \left(\log{\left(x \right)} + 2\right)^{4}}{\left(\log{\left(x \right)} + 2\right)^{4} + 1}\right)}{x^{2} \left(\left(\log{\left(x \right)} + 2\right)^{4} + 1\right)}$$
Simplify
The third derivative [src] 
  /                               3                   4                    7  \
  |                20*(2 + log(x))     12*(2 + log(x))      32*(2 + log(x))   |
2*|1 + 2*log(x) - ----------------- + ----------------- + --------------------|
  |                               4                   4                      2|
  |               1 + (2 + log(x))    1 + (2 + log(x))    /                4\ |
  \                                                       \1 + (2 + log(x)) / /
-------------------------------------------------------------------------------
                              3 /                4\                            
                             x *\1 + (2 + log(x)) /
$$\frac{2 \left(2 \log{\left(x \right)} + 1 + \frac{12 \left(\log{\left(x \right)} + 2\right)^{4}}{\left(\log{\left(x \right)} + 2\right)^{4} + 1} - \frac{20 \left(\log{\left(x \right)} + 2\right)^{3}}{\left(\log{\left(x \right)} + 2\right)^{4} + 1} + \frac{32 \left(\log{\left(x \right)} + 2\right)^{7}}{\left(\left(\log{\left(x \right)} + 2\right)^{4} + 1\right)^{2}}\right)}{x^{3} \left(\left(\log{\left(x \right)} + 2\right)^{4} + 1\right)}$$
Simplify
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