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The derivative of the function/ ((1+x^3)*arctg(x))/(7)

Derivative of ((1+x^3)*arctg(x))/(7)

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

The graph:

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The solution

You have entered [src] 
/     3\        
\1 + x /*atan(x)
----------------
       7
(x3+1)atan⁡(x)7\frac{\left(x^{3} + 1\right) \operatorname{atan}{\left(x \right)}}{7} 
((1 + x^3)*atan(x))/7
The graph
02468-8-6-4-2-1010-500500
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       3        2        
  1 + x      3*x *atan(x)
---------- + ------------
  /     2\        7      
7*\1 + x /
3x2atan⁡(x)7+x3+17(x2+1)\frac{3 x^{2} \operatorname{atan}{\left(x \right)}}{7} + \frac{x^{3} + 1}{7 \left(x^{2} + 1\right)}
Simplify
The second derivative [src] 
    /                   3          \
    |              1 + x      3*x  |
2*x*|3*atan(x) - --------- + ------|
    |                    2        2|
    |            /     2\    1 + x |
    \            \1 + x /          /
------------------------------------
                 7
2x(3xx2+1+3atan⁡(x)−x3+1(x2+1)2)7\frac{2 x \left(\frac{3 x}{x^{2} + 1} + 3 \operatorname{atan}{\left(x \right)} - \frac{x^{3} + 1}{\left(x^{2} + 1\right)^{2}}\right)}{7}
Simplify
The third derivative [src] 
  /                                          /         2 \\
  |                                 /     3\ |      4*x  ||
  |                                 \1 + x /*|-1 + ------||
  |                  3                       |          2||
  |               9*x       9*x              \     1 + x /|
2*|3*atan(x) - --------- + ------ + ----------------------|
  |                    2        2                 2       |
  |            /     2\    1 + x          /     2\        |
  \            \1 + x /                   \1 + x /        /
-----------------------------------------------------------
                             7
2(−9x3(x2+1)2+9xx2+1+3atan⁡(x)+(x3+1)(4x2x2+1−1)(x2+1)2)7\frac{2 \left(- \frac{9 x^{3}}{\left(x^{2} + 1\right)^{2}} + \frac{9 x}{x^{2} + 1} + 3 \operatorname{atan}{\left(x \right)} + \frac{\left(x^{3} + 1\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}\right)}{7}
Simplify
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