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y=arctan^3*sqrt*sin*x
Derivada de la función/ sin*x/ arctan/ y=arctan^3*sqrt*sin*x

Derivada de y=arctan^3*sqrt*sin*x

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
    3      ___       
atan (x)*\/ x *sin(x)
xatan⁡3(x)sin⁡(x)\sqrt{x} \operatorname{atan}^{3}{\left(x \right)} \sin{\left(x \right)} 
(atan(x)^3*sqrt(x))*sin(x)
Gráfica
02468-8-6-4-2-1010-2020
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Primera derivada [src] 
/    3          ___     2   \                               
|atan (x)   3*\/ x *atan (x)|            ___     3          
|-------- + ----------------|*sin(x) + \/ x *atan (x)*cos(x)
|    ___              2     |                               
\2*\/ x          1 + x      /
xcos⁡(x)atan⁡3(x)+(3xatan⁡2(x)x2+1+atan⁡3(x)2x)sin⁡(x)\sqrt{x} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} + \left(\frac{3 \sqrt{x} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{2 \sqrt{x}}\right) \sin{\left(x \right)}
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Segunda derivada [src] 
/  /    2                            ___                 \                                                                    \        
|  |atan (x)     12*atan(x)     24*\/ x *(-1 + x*atan(x))|                                                                    |        
|  |-------- - -------------- + -------------------------|*sin(x)                                                             |        
|  |   3/2       ___ /     2\                   2        |                                                                    |        
|  |  x        \/ x *\1 + x /           /     2\         |          /              ___\                                       |        
|  \                                    \1 + x /         /          |atan(x)   6*\/ x |                    ___     2          |        
|- -------------------------------------------------------------- + |------- + -------|*atan(x)*cos(x) - \/ x *atan (x)*sin(x)|*atan(x)
|                                4                                  |   ___          2|                                       |        
\                                                                   \ \/ x      1 + x /                                       /
(−xsin⁡(x)atan⁡2(x)+(6xx2+1+atan⁡(x)x)cos⁡(x)atan⁡(x)−(24x(xatan⁡(x)−1)(x2+1)2−12atan⁡(x)x(x2+1)+atan⁡2(x)x32)sin⁡(x)4)atan⁡(x)\left(- \sqrt{x} \sin{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)} + \left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{\left(\frac{24 \sqrt{x} \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}\right) \sin{\left(x \right)}}{4}\right) \operatorname{atan}{\left(x \right)}
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Tercera derivada [src] 
  /                                    /                                     2     2   \                              \                                                                                                                                                  
  |                                ___ |  1          2      6*x*atan(x)   4*x *atan (x)|                              |                                                                                                                                                  
  |                           16*\/ x *|------ - atan (x) - ----------- + -------------|                              |                                                                                                                                                  
  |    3              2                |     2                      2              2   |                              |                                                                            /    2                            ___                 \               
  |atan (x)     6*atan (x)             \1 + x                  1 + x          1 + x    /   24*(-1 + x*atan(x))*atan(x)|                                             /              ___\            |atan (x)     12*atan(x)     24*\/ x *(-1 + x*atan(x))|               
3*|-------- - ------------- + ---------------------------------------------------------- - ---------------------------|*sin(x)                                 2    |atan(x)   6*\/ x |          3*|-------- - -------------- + -------------------------|*atan(x)*cos(x)
  |   5/2      3/2 /     2\                                   2                                                2      |                                  3*atan (x)*|------- + -------|*sin(x)     |   3/2       ___ /     2\                   2        |               
  |  x        x   *\1 + x /                           /     2\                                     ___ /     2\       |                                             |   ___          2|            |  x        \/ x *\1 + x /           /     2\         |               
  \                                                   \1 + x /                                   \/ x *\1 + x /       /            ___     3                        \ \/ x      1 + x /            \                                    \1 + x /         /               
------------------------------------------------------------------------------------------------------------------------------ - \/ x *atan (x)*cos(x) - ------------------------------------- - ------------------------------------------------------------------------
                                                              8                                                                                                            2                                                        4
−xcos⁡(x)atan⁡3(x)−3(6xx2+1+atan⁡(x)x)sin⁡(x)atan⁡2(x)2−3(24x(xatan⁡(x)−1)(x2+1)2−12atan⁡(x)x(x2+1)+atan⁡2(x)x32)cos⁡(x)atan⁡(x)4+3(16x(4x2atan⁡2(x)x2+1−6xatan⁡(x)x2+1−atan⁡2(x)+1x2+1)(x2+1)2−24(xatan⁡(x)−1)atan⁡(x)x(x2+1)2−6atan⁡2(x)x32(x2+1)+atan⁡3(x)x52)sin⁡(x)8- \sqrt{x} \cos{\left(x \right)} \operatorname{atan}^{3}{\left(x \right)} - \frac{3 \left(\frac{6 \sqrt{x}}{x^{2} + 1} + \frac{\operatorname{atan}{\left(x \right)}}{\sqrt{x}}\right) \sin{\left(x \right)} \operatorname{atan}^{2}{\left(x \right)}}{2} - \frac{3 \left(\frac{24 \sqrt{x} \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \frac{12 \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}}}\right) \cos{\left(x \right)} \operatorname{atan}{\left(x \right)}}{4} + \frac{3 \left(\frac{16 \sqrt{x} \left(\frac{4 x^{2} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{6 x \operatorname{atan}{\left(x \right)}}{x^{2} + 1} - \operatorname{atan}^{2}{\left(x \right)} + \frac{1}{x^{2} + 1}\right)}{\left(x^{2} + 1\right)^{2}} - \frac{24 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \operatorname{atan}{\left(x \right)}}{\sqrt{x} \left(x^{2} + 1\right)^{2}} - \frac{6 \operatorname{atan}^{2}{\left(x \right)}}{x^{\frac{3}{2}} \left(x^{2} + 1\right)} + \frac{\operatorname{atan}^{3}{\left(x \right)}}{x^{\frac{5}{2}}}\right) \sin{\left(x \right)}}{8}
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Gráfico
Derivada de y=arctan^3*sqrt*sin*x
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