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The derivative of the function/ arctanx(sinx+2)

Derivative of arctanx(sinx+2)

Function f() - derivative -N order at the point
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The graph:

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The solution

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