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y=(arctg^3)*(4x*3^sinx)

  • ¿Cómo usar?

  • Derivada de:
  • Derivada de e^x*sin(x) Derivada de e^x*sin(x)
  • Derivada de 2*cos(3*x) Derivada de 2*cos(3*x)
  • Derivada de 1/t Derivada de 1/t
  • Derivada de x*cos(2*x) Derivada de x*cos(2*x)

  • Expresiones idénticas

  • y=(arctg^ tres)*(4x* tres ^sinx)
  • y es igual a (arctg al cubo ) multiplicar por (4x multiplicar por 3 en el grado seno de x)
  • y es igual a (arctg en el grado tres) multiplicar por (4x multiplicar por tres en el grado seno de x)
  • y=(arctg3)*(4x*3sinx)
  • y=arctg3*4x*3sinx
  • y=(arctg³)*(4x*3^sinx)
  • y=(arctg en el grado 3)*(4x*3 en el grado sinx)
  • y=(arctg^3)(4x3^sinx)
  • y=(arctg3)(4x3sinx)
  • y=arctg34x3sinx
  • y=arctg^34x3^sinx

  • Expresiones con funciones

  • arctg
  • arctg^2(1/x)
Derivada de la función/ arctg/ 3^sinx/ y=(arctg^3)*(4x*3^sinx)

Derivada de y=(arctg^3)*(4x*3^sinx)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    3         sin(x)
atan (x)*4*x*3
3sin⁡(x)4xatan⁡3(x)3^{\sin{\left(x \right)}} 4 x \operatorname{atan}^{3}{\left(x \right)} 
atan(x)^3*((4*x)*3^sin(x))
Gráfica
02468-8-6-4-2-1010-500500
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                         sin(x)     2   
    3    /   sin(x)        sin(x)              \   12*x*3      *atan (x)
atan (x)*\4*3       + 4*x*3      *cos(x)*log(3)/ + ---------------------
                                                                2       
                                                           1 + x
12⋅3sin⁡(x)xatan⁡2(x)x2+1+(4⋅3sin⁡(x)xlog⁡(3)cos⁡(x)+4⋅3sin⁡(x))atan⁡3(x)\frac{12 \cdot 3^{\sin{\left(x \right)}} x \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} + \left(4 \cdot 3^{\sin{\left(x \right)}} x \log{\left(3 \right)} \cos{\left(x \right)} + 4 \cdot 3^{\sin{\left(x \right)}}\right) \operatorname{atan}^{3}{\left(x \right)}
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Segunda derivada [src] 
   sin(x) /      2    /              /     2                   \\          6*x*(-1 + x*atan(x))   6*(1 + x*cos(x)*log(3))*atan(x)\        
4*3      *|- atan (x)*\-2*cos(x) + x*\- cos (x)*log(3) + sin(x)//*log(3) - -------------------- + -------------------------------|*atan(x)
          |                                                                             2                           2            |        
          |                                                                     /     2\                       1 + x             |        
          \                                                                     \1 + x /                                         /
4⋅3sin⁡(x)(−6x(xatan⁡(x)−1)(x2+1)2−(x(sin⁡(x)−log⁡(3)cos⁡2(x))−2cos⁡(x))log⁡(3)atan⁡2(x)+6(xlog⁡(3)cos⁡(x)+1)atan⁡(x)x2+1)atan⁡(x)4 \cdot 3^{\sin{\left(x \right)}} \left(- \frac{6 x \left(x \operatorname{atan}{\left(x \right)} - 1\right)}{\left(x^{2} + 1\right)^{2}} - \left(x \left(\sin{\left(x \right)} - \log{\left(3 \right)} \cos^{2}{\left(x \right)}\right) - 2 \cos{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}^{2}{\left(x \right)} + \frac{6 \left(x \log{\left(3 \right)} \cos{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) \operatorname{atan}{\left(x \right)}
Simplificar
Tercera derivada [src] 
          /                                                                                                         /                                     2     2   \                                                                                                                    \
          |                                                                                                         |  1          2      6*x*atan(x)   4*x *atan (x)|                                                                                                                    |
          |                                                                                                     6*x*|------ - atan (x) - ----------- + -------------|                                                                                                                    |
          |                                                                                                         |     2                      2              2   |                                                             2    /              /     2                   \\       |
   sin(x) |      3    /                2               /       2       2                     \       \              \1 + x                  1 + x          1 + x    /   18*(1 + x*cos(x)*log(3))*(-1 + x*atan(x))*atan(x)   9*atan (x)*\-2*cos(x) + x*\- cos (x)*log(3) + sin(x)//*log(3)|
4*3      *|- atan (x)*\3*sin(x) - 3*cos (x)*log(3) + x*\1 - cos (x)*log (3) + 3*log(3)*sin(x)/*cos(x)/*log(3) + ----------------------------------------------------- - ------------------------------------------------- - -------------------------------------------------------------|
          |                                                                                                                                   2                                                     2                                                        2                           |
          |                                                                                                                           /     2\                                              /     2\                                                    1 + x                            |
          \                                                                                                                           \1 + x /                                              \1 + x /                                                                                     /
4⋅3sin⁡(x)(6x(4x2atan⁡2(x)x2+1−6xatan⁡(x)x2+1−atan⁡2(x)+1x2+1)(x2+1)2−(x(3log⁡(3)sin⁡(x)−log⁡(3)2cos⁡2(x)+1)cos⁡(x)+3sin⁡(x)−3log⁡(3)cos⁡2(x))log⁡(3)atan⁡3(x)−9(x(sin⁡(x)−log⁡(3)cos⁡2(x))−2cos⁡(x))log⁡(3)atan⁡2(x)x2+1−18(xatan⁡(x)−1)(xlog⁡(3)cos⁡(x)+1)atan⁡(x)(x2+1)2)4 \cdot 3^{\sin{\left(x \right)}} \left(\frac{6 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}} - \left(x \left(3 \log{\left(3 \right)} \sin{\left(x \right)} - \log{\left(3 \right)}^{2} \cos^{2}{\left(x \right)} + 1\right) \cos{\left(x \right)} + 3 \sin{\left(x \right)} - 3 \log{\left(3 \right)} \cos^{2}{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}^{3}{\left(x \right)} - \frac{9 \left(x \left(\sin{\left(x \right)} - \log{\left(3 \right)} \cos^{2}{\left(x \right)}\right) - 2 \cos{\left(x \right)}\right) \log{\left(3 \right)} \operatorname{atan}^{2}{\left(x \right)}}{x^{2} + 1} - \frac{18 \left(x \operatorname{atan}{\left(x \right)} - 1\right) \left(x \log{\left(3 \right)} \cos{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=(arctg^3)*(4x*3^sinx)
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