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xsinxarctgx
Derivada de la función/ arctg/ xsinx/ xsinxarctgx

Derivada de xsinxarctgx

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
x*sin(x)*atan(x)
xsin⁡(x)atan⁡(x)x \sin{\left(x \right)} \operatorname{atan}{\left(x \right)} 
(x*sin(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)
(x*cos(x) + sin(x))*atan(x) + --------
                                    2 
                               1 + x
xsin⁡(x)x2+1+(xcos⁡(x)+sin⁡(x))atan⁡(x)\frac{x \sin{\left(x \right)}}{x^{2} + 1} + \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \operatorname{atan}{\left(x \right)}
Simplificar
Segunda derivada [src] 
                                                             2       
                                  2*(x*cos(x) + sin(x))   2*x *sin(x)
-(-2*cos(x) + x*sin(x))*atan(x) + --------------------- - -----------
                                               2                   2 
                                          1 + x            /     2\  
                                                           \1 + x /
−2x2sin⁡(x)(x2+1)2−(xsin⁡(x)−2cos⁡(x))atan⁡(x)+2(xcos⁡(x)+sin⁡(x))x2+1- \frac{2 x^{2} \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} + \frac{2 \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{x^{2} + 1}
Simplificar
Tercera derivada [src] 
                                                                                          /         2 \       
                                                                                          |      4*x  |       
                                                                                      2*x*|-1 + ------|*sin(x)
                                                                                          |          2|       
                                 3*(-2*cos(x) + x*sin(x))   6*x*(x*cos(x) + sin(x))       \     1 + x /       
-(3*sin(x) + x*cos(x))*atan(x) - ------------------------ - ----------------------- + ------------------------
                                               2                           2                         2        
                                          1 + x                    /     2\                  /     2\         
                                                                   \1 + x /                  \1 + x /
−6x(xcos⁡(x)+sin⁡(x))(x2+1)2+2x(4x2x2+1−1)sin⁡(x)(x2+1)2−(xcos⁡(x)+3sin⁡(x))atan⁡(x)−3(xsin⁡(x)−2cos⁡(x))x2+1- \frac{6 x \left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \operatorname{atan}{\left(x \right)} - \frac{3 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x^{2} + 1}
Simplificar
Gráfico
Derivada de xsinxarctgx
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