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Derivative of 5*sin*(x)*arctg*(x)

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

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The solution

You have entered [src]
5*sin(x)*atan(x)
$$5 \sin{\left(x \right)} \operatorname{atan}{\left(x \right)}$$
(5*sin(x))*atan(x)
The graph
The first derivative [src]
5*sin(x)                   
-------- + 5*atan(x)*cos(x)
      2                    
 1 + x                     
$$5 \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{5 \sin{\left(x \right)}}{x^{2} + 1}$$
The second derivative [src]
  /                  2*cos(x)   2*x*sin(x)\
5*|-atan(x)*sin(x) + -------- - ----------|
  |                        2            2 |
  |                   1 + x     /     2\  |
  \                             \1 + x /  /
$$5 \left(- \frac{2 x \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x^{2} + 1}\right)$$
The third derivative [src]
  /                                            /         2 \       \
  |                                            |      4*x  |       |
  |                                          2*|-1 + ------|*sin(x)|
  |                                            |          2|       |
  |                  3*sin(x)   6*x*cos(x)     \     1 + x /       |
5*|-atan(x)*cos(x) - -------- - ---------- + ----------------------|
  |                        2            2                  2       |
  |                   1 + x     /     2\           /     2\        |
  \                             \1 + x /           \1 + x /        /
$$5 \left(- \frac{6 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x^{2} + 1} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)$$