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y=x*arctan*(cos*x+5)
Derivada de la función/ arctan/ y=x*arctan*(cos*x+5)

Derivada de y=x*arctan*(cos*x+5)

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

Ha introducido [src] 
x*atan(cos(x) + 5)
xatan⁡(cos⁡(x)+5)x \operatorname{atan}{\left(\cos{\left(x \right)} + 5 \right)} 
x*atan(cos(x) + 5)
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
       x*sin(x)                       
- ----------------- + atan(cos(x) + 5)
                  2                   
  1 + (cos(x) + 5)
−xsin⁡(x)(cos⁡(x)+5)2+1+atan⁡(cos⁡(x)+5)- \frac{x \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 5\right)^{2} + 1} + \operatorname{atan}{\left(\cos{\left(x \right)} + 5 \right)}
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Segunda derivada [src] 
 /             /     2                         \\ 
 |             |2*sin (x)*(5 + cos(x))         || 
-|2*sin(x) + x*|---------------------- + cos(x)|| 
 |             |                  2            || 
 \             \  1 + (5 + cos(x))             // 
--------------------------------------------------
                                2                 
                1 + (5 + cos(x))
−x(cos⁡(x)+2(cos⁡(x)+5)sin⁡2(x)(cos⁡(x)+5)2+1)+2sin⁡(x)(cos⁡(x)+5)2+1- \frac{x \left(\cos{\left(x \right)} + \frac{2 \left(\cos{\left(x \right)} + 5\right) \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 5\right)^{2} + 1}\right) + 2 \sin{\left(x \right)}}{\left(\cos{\left(x \right)} + 5\right)^{2} + 1}
Simplificar
Tercera derivada [src] 
              /             2                        2    2                           \               2                
              |        2*sin (x)       8*(5 + cos(x)) *sin (x)   6*(5 + cos(x))*cos(x)|          6*sin (x)*(5 + cos(x))
-3*cos(x) + x*|1 + ----------------- - ----------------------- - ---------------------|*sin(x) - ----------------------
              |                    2                        2                      2  |                            2   
              |    1 + (5 + cos(x))      /                2\       1 + (5 + cos(x))   |            1 + (5 + cos(x))    
              \                          \1 + (5 + cos(x)) /                          /                                
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                                                                   2                                                   
                                                   1 + (5 + cos(x))
x(1−6(cos⁡(x)+5)cos⁡(x)(cos⁡(x)+5)2+1+2sin⁡2(x)(cos⁡(x)+5)2+1−8(cos⁡(x)+5)2sin⁡2(x)((cos⁡(x)+5)2+1)2)sin⁡(x)−3cos⁡(x)−6(cos⁡(x)+5)sin⁡2(x)(cos⁡(x)+5)2+1(cos⁡(x)+5)2+1\frac{x \left(1 - \frac{6 \left(\cos{\left(x \right)} + 5\right) \cos{\left(x \right)}}{\left(\cos{\left(x \right)} + 5\right)^{2} + 1} + \frac{2 \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 5\right)^{2} + 1} - \frac{8 \left(\cos{\left(x \right)} + 5\right)^{2} \sin^{2}{\left(x \right)}}{\left(\left(\cos{\left(x \right)} + 5\right)^{2} + 1\right)^{2}}\right) \sin{\left(x \right)} - 3 \cos{\left(x \right)} - \frac{6 \left(\cos{\left(x \right)} + 5\right) \sin^{2}{\left(x \right)}}{\left(\cos{\left(x \right)} + 5\right)^{2} + 1}}{\left(\cos{\left(x \right)} + 5\right)^{2} + 1}
Simplificar
Gráfico
Derivada de y=x*arctan*(cos*x+5)
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