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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:

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Solución

Ha introducido [src] 
      /  __________             \
      |\/ 3*sin(x)  - cos(x) + 4|
2*atan|-------------------------|
      |             ___         |
      \         2*\/ 3          /
2atan⁡((3sin⁡(x)−cos⁡(x))+423)2 \operatorname{atan}{\left(\frac{\left(\sqrt{3 \sin{\left(x \right)}} - \cos{\left(x \right)}\right) + 4}{2 \sqrt{3}} \right)} 
2*atan((sqrt(3*sin(x)) - cos(x) + 4)/((2*sqrt(3))))
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
      /  ___   ________                \
  ___ |\/ 3 *\/ sin(x) *cos(x)         |
\/ 3 *|----------------------- + sin(x)|
      \        2*sin(x)                /
----------------------------------------
    /                               2\  
    |    /  __________             \ |  
    |    \\/ 3*sin(x)  - cos(x) + 4/ |  
  3*|1 + ----------------------------|  
    \                 12             /
3(3sin⁡(x)cos⁡(x)2sin⁡(x)+sin⁡(x))3(((3sin⁡(x)−cos⁡(x))+4)212+1)\frac{\sqrt{3} \left(\frac{\sqrt{3} \sqrt{\sin{\left(x \right)}} \cos{\left(x \right)}}{2 \sin{\left(x \right)}} + \sin{\left(x \right)}\right)}{3 \left(\frac{\left(\left(\sqrt{3 \sin{\left(x \right)}} - \cos{\left(x \right)}\right) + 4\right)^{2}}{12} + 1\right)}
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Segunda derivada [src] 
       /                                                                            2                                \ 
       |                                                   /             ___       \                                 | 
       |                                                   |           \/ 3 *cos(x)|  /               ___   ________\| 
       |                                                 2*|2*sin(x) + ------------| *\4 - cos(x) + \/ 3 *\/ sin(x) /| 
       |                                   ___    2        |              ________ |                                 | 
   ___ |                ___   ________   \/ 3 *cos (x)     \            \/ sin(x)  /                                 | 
-\/ 3 *|-4*cos(x) + 2*\/ 3 *\/ sin(x)  + ------------- + ------------------------------------------------------------| 
       |                                      3/2                                                       2            | 
       |                                   sin   (x)                     /               ___   ________\             | 
       \                                                            12 + \4 - cos(x) + \/ 3 *\/ sin(x) /             / 
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                                                                             2                                         
                                              /               ___   ________\                                          
                                         12 + \4 - cos(x) + \/ 3 *\/ sin(x) /
−3(23sin⁡(x)−4cos⁡(x)+3cos⁡2(x)sin⁡32(x)+2(2sin⁡(x)+3cos⁡(x)sin⁡(x))2(3sin⁡(x)−cos⁡(x)+4)(3sin⁡(x)−cos⁡(x)+4)2+12)(3sin⁡(x)−cos⁡(x)+4)2+12- \frac{\sqrt{3} \left(2 \sqrt{3} \sqrt{\sin{\left(x \right)}} - 4 \cos{\left(x \right)} + \frac{\sqrt{3} \cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}} + \frac{2 \left(2 \sin{\left(x \right)} + \frac{\sqrt{3} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\right)^{2} \left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)}{\left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)^{2} + 12}\right)}{\left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)^{2} + 12}
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Tercera derivada [src] 
      /                                            3                                                                     3                                                                                                                                                \
      |                   /             ___       \                                             /             ___       \                                 2     /             ___       \                                 /                                   ___    2   \|
      |                   |           \/ 3 *cos(x)|                                             |           \/ 3 *cos(x)|  /               ___   ________\      |           \/ 3 *cos(x)| /               ___   ________\ |                ___   ________   \/ 3 *cos (x)||
      |                 2*|2*sin(x) + ------------|                                           8*|2*sin(x) + ------------| *\4 - cos(x) + \/ 3 *\/ sin(x) /    6*|2*sin(x) + ------------|*\4 - cos(x) + \/ 3 *\/ sin(x) /*|-4*cos(x) + 2*\/ 3 *\/ sin(x)  + -------------||
      |                   |              ________ |            ___              ___    3        |              ________ |                                       |              ________ |                                 |                                      3/2     ||
  ___ |                   \            \/ sin(x)  /        2*\/ 3 *cos(x)   3*\/ 3 *cos (x)     \            \/ sin(x)  /                                       \            \/ sin(x)  /                                 \                                   sin   (x)  /|
\/ 3 *|-8*sin(x) - ------------------------------------- + -------------- + --------------- + ------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------|
      |                                                2       ________           5/2                                                           2                                                                                    2                                    |
      |                 /               ___   ________\      \/ sin(x)         sin   (x)                 /                                    2\                                                      /               ___   ________\                                     |
      |            12 + \4 - cos(x) + \/ 3 *\/ sin(x) /                                                  |     /               ___   ________\ |                                                 12 + \4 - cos(x) + \/ 3 *\/ sin(x) /                                     |
      \                                                                                                  \12 + \4 - cos(x) + \/ 3 *\/ sin(x) / /                                                                                                                          /
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                                                                                                                   /                                    2\                                                                                                                 
                                                                                                                   |     /               ___   ________\ |                                                                                                                 
                                                                                                                 2*\12 + \4 - cos(x) + \/ 3 *\/ sin(x) / /
3(−8sin⁡(x)+23cos⁡(x)sin⁡(x)+33cos⁡3(x)sin⁡52(x)−2(2sin⁡(x)+3cos⁡(x)sin⁡(x))3(3sin⁡(x)−cos⁡(x)+4)2+12+6(2sin⁡(x)+3cos⁡(x)sin⁡(x))(3sin⁡(x)−cos⁡(x)+4)(23sin⁡(x)−4cos⁡(x)+3cos⁡2(x)sin⁡32(x))(3sin⁡(x)−cos⁡(x)+4)2+12+8(2sin⁡(x)+3cos⁡(x)sin⁡(x))3(3sin⁡(x)−cos⁡(x)+4)2((3sin⁡(x)−cos⁡(x)+4)2+12)2)2((3sin⁡(x)−cos⁡(x)+4)2+12)\frac{\sqrt{3} \left(- 8 \sin{\left(x \right)} + \frac{2 \sqrt{3} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}} + \frac{3 \sqrt{3} \cos^{3}{\left(x \right)}}{\sin^{\frac{5}{2}}{\left(x \right)}} - \frac{2 \left(2 \sin{\left(x \right)} + \frac{\sqrt{3} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\right)^{3}}{\left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)^{2} + 12} + \frac{6 \left(2 \sin{\left(x \right)} + \frac{\sqrt{3} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\right) \left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right) \left(2 \sqrt{3} \sqrt{\sin{\left(x \right)}} - 4 \cos{\left(x \right)} + \frac{\sqrt{3} \cos^{2}{\left(x \right)}}{\sin^{\frac{3}{2}}{\left(x \right)}}\right)}{\left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)^{2} + 12} + \frac{8 \left(2 \sin{\left(x \right)} + \frac{\sqrt{3} \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)}}}\right)^{3} \left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)^{2}}{\left(\left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)^{2} + 12\right)^{2}}\right)}{2 \left(\left(\sqrt{3} \sqrt{\sin{\left(x \right)}} - \cos{\left(x \right)} + 4\right)^{2} + 12\right)}
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Gráfico
Derivada de y=2arctg((√3sinx-cosx+4)/(2√3))
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