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y=2arctg(√3sinx-cosx+4/2√3)
Derivada de la función/ y=2arctg(√3sinx-cosx+4/2√3)

Derivada de y=2arctg(√3sinx-cosx+4/2√3)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
      /  ___                       ___\
2*atan\\/ 3 *sin(x) - cos(x) + 2*\/ 3 /
2atan⁡((3sin⁡(x)−cos⁡(x))+23)2 \operatorname{atan}{\left(\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)}\right) + 2 \sqrt{3} \right)} 
2*atan(sqrt(3)*sin(x) - cos(x) + 2*sqrt(3))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        /  ___                \       
      2*\\/ 3 *cos(x) + sin(x)/       
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                                     2
    /  ___                       ___\ 
1 + \\/ 3 *sin(x) - cos(x) + 2*\/ 3 /
2(sin⁡(x)+3cos⁡(x))((3sin⁡(x)−cos⁡(x))+23)2+1\frac{2 \left(\sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}\right)}{\left(\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)}\right) + 2 \sqrt{3}\right)^{2} + 1}
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Segunda derivada [src] 
   /                                                  2                                   \
   |                           /  ___                \  /              ___     ___       \|
   |            ___          2*\\/ 3 *cos(x) + sin(x)/ *\-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/|
-2*|-cos(x) + \/ 3 *sin(x) + -------------------------------------------------------------|
   |                                                                          2           |
   |                                        /              ___     ___       \            |
   \                                    1 + \-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/            /
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                                                                2                          
                              /              ___     ___       \                           
                          1 + \-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/
−2(3sin⁡(x)−cos⁡(x)+2(sin⁡(x)+3cos⁡(x))2(3sin⁡(x)−cos⁡(x)+23)(3sin⁡(x)−cos⁡(x)+23)2+1)(3sin⁡(x)−cos⁡(x)+23)2+1- \frac{2 \left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + \frac{2 \left(\sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}\right)^{2} \left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)}{\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)^{2} + 1}\right)}{\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)^{2} + 1}
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Tercera derivada [src] 
                          /                                     2                                                                                                  2                                   2\
                          |              /  ___                \            /            ___       \ /              ___     ___       \     /  ___                \  /              ___     ___       \ |
  /  ___                \ |            2*\\/ 3 *cos(x) + sin(x)/          6*\-cos(x) + \/ 3 *sin(x)/*\-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/   8*\\/ 3 *cos(x) + sin(x)/ *\-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/ |
2*\\/ 3 *cos(x) + sin(x)/*|-1 - --------------------------------------- + ------------------------------------------------------------- + --------------------------------------------------------------|
                          |                                           2                                                    2                                                                 2          |
                          |         /              ___     ___       \                   /              ___     ___       \                         /                                      2\           |
                          |     1 + \-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/               1 + \-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/                         |    /              ___     ___       \ |           |
                          \                                                                                                                         \1 + \-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/ /           /
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                                                                                                                       2                                                                                 
                                                                                     /              ___     ___       \                                                                                  
                                                                                 1 + \-cos(x) + 2*\/ 3  + \/ 3 *sin(x)/
2(sin⁡(x)+3cos⁡(x))(6(3sin⁡(x)−cos⁡(x))(3sin⁡(x)−cos⁡(x)+23)(3sin⁡(x)−cos⁡(x)+23)2+1−1−2(sin⁡(x)+3cos⁡(x))2(3sin⁡(x)−cos⁡(x)+23)2+1+8(sin⁡(x)+3cos⁡(x))2(3sin⁡(x)−cos⁡(x)+23)2((3sin⁡(x)−cos⁡(x)+23)2+1)2)(3sin⁡(x)−cos⁡(x)+23)2+1\frac{2 \left(\sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}\right) \left(\frac{6 \left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)}\right) \left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)}{\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)^{2} + 1} - 1 - \frac{2 \left(\sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}\right)^{2}}{\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)^{2} + 1} + \frac{8 \left(\sin{\left(x \right)} + \sqrt{3} \cos{\left(x \right)}\right)^{2} \left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)^{2}}{\left(\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)^{2} + 1\right)^{2}}\right)}{\left(\sqrt{3} \sin{\left(x \right)} - \cos{\left(x \right)} + 2 \sqrt{3}\right)^{2} + 1}
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Gráfico
Derivada de y=2arctg(√3sinx-cosx+4/2√3)
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