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(-x*sin(x)+cos(x))*arctan(x)
Derivada de la función/ x*sin(x)+cos(x)/ (-x*sin(x)+cos(x))*arctan(x)

Derivada de (-x*sin(x)+cos(x))*arctan(x)

Función f() - derivada -er orden en el punto
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Solución

Ha introducido [src] 
(-x*sin(x) + cos(x))*atan(x)
(−xsin⁡(x)+cos⁡(x))atan⁡(x)\left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} 
((-x)*sin(x) + cos(x))*atan(x)
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
-x*sin(x) + cos(x)                                 
------------------ + (-2*sin(x) - x*cos(x))*atan(x)
           2                                       
      1 + x
(−xcos⁡(x)−2sin⁡(x))atan⁡(x)+−xsin⁡(x)+cos⁡(x)x2+1\left(- x \cos{\left(x \right)} - 2 \sin{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{- x \sin{\left(x \right)} + \cos{\left(x \right)}}{x^{2} + 1}
Simplificar
Segunda derivada [src] 
                                 2*(2*sin(x) + x*cos(x))   2*x*(-x*sin(x) + cos(x))
(-3*cos(x) + x*sin(x))*atan(x) - ----------------------- - ------------------------
                                               2                          2        
                                          1 + x                   /     2\         
                                                                  \1 + x /
−2x(−xsin⁡(x)+cos⁡(x))(x2+1)2+(xsin⁡(x)−3cos⁡(x))atan⁡(x)−2(xcos⁡(x)+2sin⁡(x))x2+1- \frac{2 x \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} + \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} - \frac{2 \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{x^{2} + 1}
Simplificar
Tercera derivada [src] 
                                                             /         2 \                                                 
                                                             |      4*x  |                                                 
                                                           2*|-1 + ------|*(-x*sin(x) + cos(x))                            
                                                             |          2|                                                 
                                3*(-3*cos(x) + x*sin(x))     \     1 + x /                        6*x*(2*sin(x) + x*cos(x))
(4*sin(x) + x*cos(x))*atan(x) + ------------------------ + ------------------------------------ + -------------------------
                                              2                                 2                                 2        
                                         1 + x                          /     2\                          /     2\         
                                                                        \1 + x /                          \1 + x /
6x(xcos⁡(x)+2sin⁡(x))(x2+1)2+(xcos⁡(x)+4sin⁡(x))atan⁡(x)+3(xsin⁡(x)−3cos⁡(x))x2+1+2(−xsin⁡(x)+cos⁡(x))(4x2x2+1−1)(x2+1)2\frac{6 x \left(x \cos{\left(x \right)} + 2 \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} + \left(x \cos{\left(x \right)} + 4 \sin{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{3 \left(x \sin{\left(x \right)} - 3 \cos{\left(x \right)}\right)}{x^{2} + 1} + \frac{2 \left(- x \sin{\left(x \right)} + \cos{\left(x \right)}\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right)}{\left(x^{2} + 1\right)^{2}}
Simplificar
Gráfico
Derivada de (-x*sin(x)+cos(x))*arctan(x)
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