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y=(tgx)^(1/2)(ln)arctg(x)
Derivada de la función/ tg(x)/ arctg/ (1/2)/ (tgx)/ y=(tgx)^(1/2)(ln)arctg(x)

Derivada de y=(tgx)^(1/2)(ln)arctg(x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
  ________               
\/ tan(x) *log(x)*atan(x)
log⁡(x)tan⁡(x)atan⁡(x)\log{\left(x \right)} \sqrt{\tan{\left(x \right)}} \operatorname{atan}{\left(x \right)} 
(sqrt(tan(x))*log(x))*atan(x)
Gráfica
02468-8-6-4-2-1010-100100
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Trazar el gráfico f'(x)
Primera derivada [src] 
/             /       2   \       \                            
|             |1   tan (x)|       |                            
|  ________   |- + -------|*log(x)|             ________       
|\/ tan(x)    \2      2   /       |           \/ tan(x) *log(x)
|---------- + --------------------|*atan(x) + -----------------
|    x               ________     |                      2     
\                  \/ tan(x)      /                 1 + x
((tan⁡2(x)2+12)log⁡(x)tan⁡(x)+tan⁡(x)x)atan⁡(x)+log⁡(x)tan⁡(x)x2+1\left(\frac{\left(\frac{\tan^{2}{\left(x \right)}}{2} + \frac{1}{2}\right) \log{\left(x \right)}}{\sqrt{\tan{\left(x \right)}}} + \frac{\sqrt{\tan{\left(x \right)}}}{x}\right) \operatorname{atan}{\left(x \right)} + \frac{\log{\left(x \right)} \sqrt{\tan{\left(x \right)}}}{x^{2} + 1}
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Segunda derivada [src] 
    ________   /       2   \          /    ________                 /                        2   \            /       2   \\                                
2*\/ tan(x)    \1 + tan (x)/*log(x)   |4*\/ tan(x)    /       2   \ |      ________   1 + tan (x)|          4*\1 + tan (x)/|                                
------------ + --------------------   |------------ + \1 + tan (x)/*|- 4*\/ tan(x)  + -----------|*log(x) - ---------------|*atan(x)                        
     x                ________        |      2                      |                     3/2    |                ________ |                 ________       
                    \/ tan(x)         \     x                       \                  tan   (x) /            x*\/ tan(x)  /           2*x*\/ tan(x) *log(x)
----------------------------------- - ---------------------------------------------------------------------------------------------- - ---------------------
                    2                                                               4                                                                2      
               1 + x                                                                                                                         /     2\       
                                                                                                                                             \1 + x /
−2xlog⁡(x)tan⁡(x)(x2+1)2−((tan⁡2(x)+1tan⁡32(x)−4tan⁡(x))(tan⁡2(x)+1)log⁡(x)−4(tan⁡2(x)+1)xtan⁡(x)+4tan⁡(x)x2)atan⁡(x)4+(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2tan⁡(x)xx2+1- \frac{2 x \log{\left(x \right)} \sqrt{\tan{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}} - \frac{\left(\left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \sqrt{\tan{\left(x \right)}}} + \frac{4 \sqrt{\tan{\left(x \right)}}}{x^{2}}\right) \operatorname{atan}{\left(x \right)}}{4} + \frac{\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\tan{\left(x \right)}}} + \frac{2 \sqrt{\tan{\left(x \right)}}}{x}}{x^{2} + 1}
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Tercera derivada [src] 
                                                                                             /                                                                                                                              /                        2   \\                                                                                        
                                                                                             |                                                                                                                /       2   \ |      ________   1 + tan (x)||                                                                                        
                                                                                             |                              /                                                2\                             6*\1 + tan (x)/*|- 4*\/ tan(x)  + -----------||                                                                                        
    /    ________                 /                        2   \            /       2   \\   |     ________                 |                 /       2   \     /       2   \ |             /       2   \                   |                     3/2    ||               /    ________   /       2   \       \                /         2 \       
    |4*\/ tan(x)    /       2   \ |      ________   1 + tan (x)|          4*\1 + tan (x)/|   |16*\/ tan(x)    /       2   \ |      3/2      4*\1 + tan (x)/   3*\1 + tan (x)/ |          12*\1 + tan (x)/                   \                  tan   (x) /|               |2*\/ tan(x)    \1 + tan (x)/*log(x)|       ________ |      4*x  |       
  3*|------------ + \1 + tan (x)/*|- 4*\/ tan(x)  + -----------|*log(x) - ---------------|   |------------- + \1 + tan (x)/*|16*tan   (x) - --------------- + ----------------|*log(x) - ---------------- - ----------------------------------------------|*atan(x)   3*x*|------------ + --------------------|   2*\/ tan(x) *|-1 + ------|*log(x)
    |      2                      |                     3/2    |                ________ |   |       3                      |                    ________           5/2       |            2   ________                           x                       |               |     x                ________     |                |          2|       
    \     x                       \                  tan   (x) /            x*\/ tan(x)  /   \      x                       \                  \/ tan(x)         tan   (x)    /           x *\/ tan(x)                                                    /               \                    \/ tan(x)      /                \     1 + x /       
- ---------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------- + ---------------------------------
                                           /     2\                                                                                                                            8                                                                                                              2                                       2            
                                         4*\1 + x /                                                                                                                                                                                                                                   /     2\                                /     2\             
                                                                                                                                                                                                                                                                                      \1 + x /                                \1 + x /
−3x((tan⁡2(x)+1)log⁡(x)tan⁡(x)+2tan⁡(x)x)(x2+1)2+((tan⁡2(x)+1)(3(tan⁡2(x)+1)2tan⁡52(x)−4(tan⁡2(x)+1)tan⁡(x)+16tan⁡32(x))log⁡(x)−6(tan⁡2(x)+1tan⁡32(x)−4tan⁡(x))(tan⁡2(x)+1)x−12(tan⁡2(x)+1)x2tan⁡(x)+16tan⁡(x)x3)atan⁡(x)8−3((tan⁡2(x)+1tan⁡32(x)−4tan⁡(x))(tan⁡2(x)+1)log⁡(x)−4(tan⁡2(x)+1)xtan⁡(x)+4tan⁡(x)x2)4(x2+1)+2(4x2x2+1−1)log⁡(x)tan⁡(x)(x2+1)2- \frac{3 x \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\sqrt{\tan{\left(x \right)}}} + \frac{2 \sqrt{\tan{\left(x \right)}}}{x}\right)}{\left(x^{2} + 1\right)^{2}} + \frac{\left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{\frac{5}{2}}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\sqrt{\tan{\left(x \right)}}} + 16 \tan^{\frac{3}{2}}{\left(x \right)}\right) \log{\left(x \right)} - \frac{6 \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} \sqrt{\tan{\left(x \right)}}} + \frac{16 \sqrt{\tan{\left(x \right)}}}{x^{3}}\right) \operatorname{atan}{\left(x \right)}}{8} - \frac{3 \left(\left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan^{\frac{3}{2}}{\left(x \right)}} - 4 \sqrt{\tan{\left(x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \sqrt{\tan{\left(x \right)}}} + \frac{4 \sqrt{\tan{\left(x \right)}}}{x^{2}}\right)}{4 \left(x^{2} + 1\right)} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \log{\left(x \right)} \sqrt{\tan{\left(x \right)}}}{\left(x^{2} + 1\right)^{2}}
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Gráfico
Derivada de y=(tgx)^(1/2)(ln)arctg(x)
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