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The derivative of the function/ x*arctg(x)+sin(x)

Derivative of x*arctg(x)+sin(x)

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

The graph:

from to

Piecewise:

The solution

You have entered [src] 
x*atan(x) + sin(x)
$$x \operatorname{atan}{\left(x \right)} + \sin{\left(x \right)}$$ 
x*atan(x) + sin(x)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  x                      
------ + atan(x) + cos(x)
     2                   
1 + x
$$\frac{x}{x^{2} + 1} + \cos{\left(x \right)} + \operatorname{atan}{\left(x \right)}$$
Simplify
The second derivative [src] 
                         2  
            2         2*x   
-sin(x) + ------ - ---------
               2           2
          1 + x    /     2\ 
                   \1 + x /
$$- \frac{2 x^{2}}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} + \frac{2}{x^{2} + 1}$$
Simplify
The third derivative [src] 
                            3  
             8*x         8*x   
-cos(x) - --------- + ---------
                  2           3
          /     2\    /     2\ 
          \1 + x /    \1 + x /
$$\frac{8 x^{3}}{\left(x^{2} + 1\right)^{3}} - \frac{8 x}{\left(x^{2} + 1\right)^{2}} - \cos{\left(x \right)}$$
Simplify
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