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arctg^2(3x)
The derivative of the function/ arctg^2(3x)

Derivative of arctg^2(3x)

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

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The solution

You have entered [src] 
    2     
atan (3*x)
$$\operatorname{atan}^{2}{\left(3 x \right)}$$ 
atan(3*x)^2
The graph
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The first derivative [src] 
6*atan(3*x)
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         2 
  1 + 9*x
$$\frac{6 \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1}$$
Simplify
The second derivative [src] 
18*(1 - 6*x*atan(3*x))
----------------------
               2      
     /       2\       
     \1 + 9*x /
$$\frac{18 \left(- 6 x \operatorname{atan}{\left(3 x \right)} + 1\right)}{\left(9 x^{2} + 1\right)^{2}}$$
Simplify
The third derivative [src] 
    /                            2          \
    |               9*x      36*x *atan(3*x)|
108*|-atan(3*x) - -------- + ---------------|
    |                    2              2   |
    \             1 + 9*x        1 + 9*x    /
---------------------------------------------
                           2                 
                 /       2\                  
                 \1 + 9*x /
$$\frac{108 \left(\frac{36 x^{2} \operatorname{atan}{\left(3 x \right)}}{9 x^{2} + 1} - \frac{9 x}{9 x^{2} + 1} - \operatorname{atan}{\left(3 x \right)}\right)}{\left(9 x^{2} + 1\right)^{2}}$$
Simplify
The graph
Derivative of arctg^2(3x)
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