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y=arctg(3x*e^√tgx)
Derivada de la función/ arctg/ y=arctg(3x*e^√tgx)

Derivada de y=arctg(3x*e^√tgx)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /       ________\
    |     \/ tan(x) |
atan\3*x*E          /
atan⁡(etan⁡(x)3x)\operatorname{atan}{\left(e^{\sqrt{\tan{\left(x \right)}}} 3 x \right)} 
atan((3*x)*E^(sqrt(tan(x))))
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
                    /       2   \    ________
                    |1   tan (x)|  \/ tan(x) 
     ________   3*x*|- + -------|*e          
   \/ tan(x)        \2      2   /            
3*e           + -----------------------------
                            ________         
                          \/ tan(x)          
---------------------------------------------
                          ________           
                   2  2*\/ tan(x)            
            1 + 9*x *e
3x(tan⁡2(x)2+12)etan⁡(x)tan⁡(x)+3etan⁡(x)9x2e2tan⁡(x)+1\frac{\frac{3 x \left(\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}\right) e^{\sqrt{\tan{\left(x \right)}}}}{\sqrt{\tan{\left(x \right)}}} + 3 e^{\sqrt{\tan{\left(x \right)}}}}{9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1}
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Segunda derivada [src] 
  /                                                                                                            2              \            
  |                                                                                       /      /       2   \\       ________|            
  |                                                                                       |    x*\1 + tan (x)/|   2*\/ tan(x) |            
  |                                                                                  18*x*|2 + ---------------| *e            |            
  |              /                                /       2   \     /       2   \\        |         ________  |               |    ________
  |/       2   \ |    4              ________   x*\1 + tan (x)/   x*\1 + tan (x)/|        \       \/ tan(x)   /               |  \/ tan(x) 
3*|\1 + tan (x)/*|---------- + 4*x*\/ tan(x)  + --------------- - ---------------| - -----------------------------------------|*e          
  |              |  ________                         tan(x)             3/2      |                           ________         |            
  |              \\/ tan(x)                                          tan   (x)   /                    2  2*\/ tan(x)          |            
  \                                                                                            1 + 9*x *e                     /            
-------------------------------------------------------------------------------------------------------------------------------------------
                                                           /              ________\                                                        
                                                           |       2  2*\/ tan(x) |                                                        
                                                         4*\1 + 9*x *e            /
3(−18x(x(tan⁡2(x)+1)tan⁡(x)+2)2e2tan⁡(x)9x2e2tan⁡(x)+1+(tan⁡2(x)+1)(x(tan⁡2(x)+1)tan⁡(x)−x(tan⁡2(x)+1)tan⁡32(x)+4xtan⁡(x)+4tan⁡(x)))etan⁡(x)4(9x2e2tan⁡(x)+1)\frac{3 \left(- \frac{18 x \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{2} e^{2 \sqrt{\tan{\left(x \right)}}}}{9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{\frac{3}{2}}{\left(x \right)}} + 4 x \sqrt{\tan{\left(x \right)}} + \frac{4}{\sqrt{\tan{\left(x \right)}}}\right)\right) e^{\sqrt{\tan{\left(x \right)}}}}{4 \left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)}
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Tercera derivada [src] 
  /              /                                                                                                         2                                        2                    2\                              3                                         /                    2                     2                                                    \                                                                                                                                        \            
  |              |                  /       2   \     /       2   \                                           /       2   \        /       2   \       /       2   \        /       2   \ |         /      /       2   \\       ________     /      /       2   \\ |     2 /       2   \       2 /       2   \                                        /       2   \|      ________                     /      /       2   \\ /                                /       2   \     /       2   \\      ________|            
  |/       2   \ |     ________   6*\1 + tan (x)/   6*\1 + tan (x)/        /       2   \           3/2      x*\1 + tan (x)/    4*x*\1 + tan (x)/   3*x*\1 + tan (x)/    3*x*\1 + tan (x)/ |       2 |    x*\1 + tan (x)/|   4*\/ tan(x)      |    x*\1 + tan (x)/| |    x *\1 + tan (x)/    2*x *\1 + tan (x)/       2   ________ /       2   \   8*x*\1 + tan (x)/|  2*\/ tan(x)        /       2   \ |    x*\1 + tan (x)/| |    4              ________   x*\1 + tan (x)/   x*\1 + tan (x)/|  2*\/ tan(x) |            
  |\1 + tan (x)/*|24*\/ tan(x)  - --------------- + --------------- + 12*x*\1 + tan (x)/ + 16*x*tan   (x) + ---------------- - ----------------- - ------------------ + ------------------|   81*x *|2 + ---------------| *e               9*|2 + ---------------|*|4 - ----------------- + ------------------- + 4*x *\/ tan(x) *\1 + tan (x)/ + -----------------|*e               9*x*\1 + tan (x)/*|2 + ---------------|*|---------- + 4*x*\/ tan(x)  + --------------- - ---------------|*e            |            
  |              |                      3/2              tan(x)                                                   3/2                ________              2                   5/2        |         |         ________  |                    |         ________  | |           3/2                 tan(x)                                               ________   |                                   |         ________  | |  ________                         tan(x)             3/2      |              |    ________
  |              \                   tan   (x)                                                                 tan   (x)           \/ tan(x)            tan (x)             tan   (x)     /         \       \/ tan(x)   /                    \       \/ tan(x)   / \        tan   (x)                                                                 \/ tan(x)    /                                   \       \/ tan(x)   / \\/ tan(x)                                          tan   (x)   /              |  \/ tan(x) 
3*|---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------ - --------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------|*e          
  |                                                                                           8                                                                                                                               2                                                                     /              ________\                                                                                                          /              ________\                                              |            
  |                                                                                                                                                                                                   /              ________\                                                                      |       2  2*\/ tan(x) |                                                                                                          |       2  2*\/ tan(x) |                                              |            
  |                                                                                                                                                                                                   |       2  2*\/ tan(x) |                                                                    4*\1 + 9*x *e            /                                                                                                        2*\1 + 9*x *e            /                                              |            
  \                                                                                                                                                                                                   \1 + 9*x *e            /                                                                                                                                                                                                                                                                              /            
-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                ________                                                                                                                                                                                                                                                 
                                                                                                                                                                                                                                                         2  2*\/ tan(x)                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                  1 + 9*x *e
3(81x2(x(tan⁡2(x)+1)tan⁡(x)+2)3e4tan⁡(x)(9x2e2tan⁡(x)+1)2−9x(x(tan⁡2(x)+1)tan⁡(x)+2)(tan⁡2(x)+1)(x(tan⁡2(x)+1)tan⁡(x)−x(tan⁡2(x)+1)tan⁡32(x)+4xtan⁡(x)+4tan⁡(x))e2tan⁡(x)2(9x2e2tan⁡(x)+1)+(tan⁡2(x)+1)(−3x(tan⁡2(x)+1)2tan⁡2(x)+x(tan⁡2(x)+1)2tan⁡32(x)+3x(tan⁡2(x)+1)2tan⁡52(x)+12x(tan⁡2(x)+1)−4x(tan⁡2(x)+1)tan⁡(x)+16xtan⁡32(x)+6(tan⁡2(x)+1)tan⁡(x)−6(tan⁡2(x)+1)tan⁡32(x)+24tan⁡(x))8−9(x(tan⁡2(x)+1)tan⁡(x)+2)(2x2(tan⁡2(x)+1)2tan⁡(x)−x2(tan⁡2(x)+1)2tan⁡32(x)+4x2(tan⁡2(x)+1)tan⁡(x)+8x(tan⁡2(x)+1)tan⁡(x)+4)e2tan⁡(x)4(9x2e2tan⁡(x)+1))etan⁡(x)9x2e2tan⁡(x)+1\frac{3 \left(\frac{81 x^{2} \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right)^{3} e^{4 \sqrt{\tan{\left(x \right)}}}}{\left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)^{2}} - \frac{9 x \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{\frac{3}{2}}{\left(x \right)}} + 4 x \sqrt{\tan{\left(x \right)}} + \frac{4}{\sqrt{\tan{\left(x \right)}}}\right) e^{2 \sqrt{\tan{\left(x \right)}}}}{2 \left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} + \frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x \right)}} + 12 x \left(\tan^{2}{\left(x \right)} + 1\right) - \frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 16 x \tan^{\frac{3}{2}}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{\frac{3}{2}}{\left(x \right)}} + 24 \sqrt{\tan{\left(x \right)}}\right)}{8} - \frac{9 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 2\right) \left(\frac{2 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} - \frac{x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{3}{2}}{\left(x \right)}} + 4 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right) \sqrt{\tan{\left(x \right)}} + \frac{8 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 4\right) e^{2 \sqrt{\tan{\left(x \right)}}}}{4 \left(9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1\right)}\right) e^{\sqrt{\tan{\left(x \right)}}}}{9 x^{2} e^{2 \sqrt{\tan{\left(x \right)}}} + 1}
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Gráfico
Derivada de y=arctg(3x*e^√tgx)
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