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y=arctanh(logtan(x))
Derivada de la función/ tan(x)/ arctan/ y=arctanh(logtan(x))

Derivada de y=arctanh(logtan(x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
atanh(log(x)*tan(x))
atanh⁡(log⁡(x)tan⁡(x))\operatorname{atanh}{\left(\log{\left(x \right)} \tan{\left(x \right)} \right)} 
atanh(log(x)*tan(x))
Gráfica
02468-8-6-4-2-1010-250250
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
tan(x)   /       2   \       
------ + \1 + tan (x)/*log(x)
  x                          
-----------------------------
            2       2        
     1 - log (x)*tan (x)
(tan⁡2(x)+1)log⁡(x)+tan⁡(x)x−log⁡(x)2tan⁡2(x)+1\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}}{- \log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} + 1}
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Segunda derivada [src] 
                                                                                            2              
                                                             /tan(x)   /       2   \       \               
           /       2   \                                   2*|------ + \1 + tan (x)/*log(x)| *log(x)*tan(x)
tan(x)   2*\1 + tan (x)/     /       2   \                   \  x                          /               
------ - --------------- - 2*\1 + tan (x)/*log(x)*tan(x) + ------------------------------------------------
   2            x                                                                2       2                 
  x                                                                      -1 + log (x)*tan (x)              
-----------------------------------------------------------------------------------------------------------
                                                    2       2                                              
                                            -1 + log (x)*tan (x)
2((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2log⁡(x)tan⁡(x)log⁡(x)2tan⁡2(x)−1−2(tan⁡2(x)+1)log⁡(x)tan⁡(x)−2(tan⁡2(x)+1)x+tan⁡(x)x2log⁡(x)2tan⁡2(x)−1\frac{\frac{2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} \log{\left(x \right)} \tan{\left(x \right)}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} + \frac{\tan{\left(x \right)}}{x^{2}}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1}
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Tercera derivada [src] 
                                                                                                                                                     /   2                   2              2                                                 /       2   \              \                                                                                          /             /       2   \                                \              
                                                                                                                     /tan(x)   /       2   \       \ |tan (x)   /       2   \     2      tan (x)*log(x)        2       2    /       2   \   4*\1 + tan (x)/*log(x)*tan(x)|                                    3                     /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |              
                                                                                                                   2*|------ + \1 + tan (x)/*log(x)|*|------- + \1 + tan (x)/ *log (x) - -------------- + 2*log (x)*tan (x)*\1 + tan (x)/ + -----------------------------|     /tan(x)   /       2   \       \     2       2      4*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|*log(x)*tan(x)
                            2            /       2   \     /       2   \                                             \  x                          / |    2                                     2                                                         x              |   8*|------ + \1 + tan (x)/*log(x)| *log (x)*tan (x)     \  x                          / |     2            x                                       |              
  2*tan(x)     /       2   \           3*\1 + tan (x)/   6*\1 + tan (x)/*tan(x)        2    /       2   \                                            \   x                                     x                                                                         /     \  x                          /                                                      \    x                                                     /              
- -------- - 2*\1 + tan (x)/ *log(x) + --------------- - ---------------------- - 4*tan (x)*\1 + tan (x)/*log(x) + ------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------- + ------------------------------------------------------------------------------------------------------------
      3                                        2                   x                                                                                                                         2       2                                                                                                          2                                                                     2       2                                               
     x                                        x                                                                                                                                      -1 + log (x)*tan (x)                                                                                 /        2       2   \                                                              -1 + log (x)*tan (x)                                            
                                                                                                                                                                                                                                                                                          \-1 + log (x)*tan (x)/                                                                                                                              
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                     2       2                                                                                                                                                                                                                
                                                                                                                                                                                                             -1 + log (x)*tan (x)
−8((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)3log⁡(x)2tan⁡2(x)(log⁡(x)2tan⁡2(x)−1)2+4((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)(2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)log⁡(x)tan⁡(x)log⁡(x)2tan⁡2(x)−1+2((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)((tan⁡2(x)+1)2log⁡(x)2+2(tan⁡2(x)+1)log⁡(x)2tan⁡2(x)+4(tan⁡2(x)+1)log⁡(x)tan⁡(x)x−log⁡(x)tan⁡2(x)x2+tan⁡2(x)x2)log⁡(x)2tan⁡2(x)−1−2(tan⁡2(x)+1)2log⁡(x)−4(tan⁡2(x)+1)log⁡(x)tan⁡2(x)−6(tan⁡2(x)+1)tan⁡(x)x+3(tan⁡2(x)+1)x2−2tan⁡(x)x3log⁡(x)2tan⁡2(x)−1\frac{- \frac{8 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} \log{\left(x \right)}^{2} \tan^{2}{\left(x \right)}}{\left(\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1\right)^{2}} + \frac{4 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right) \log{\left(x \right)} \tan{\left(x \right)}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1} + \frac{2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)}}{x} - \frac{\log{\left(x \right)} \tan^{2}{\left(x \right)}}{x^{2}} + \frac{\tan^{2}{\left(x \right)}}{x^{2}}\right)}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1} - 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)} - 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan^{2}{\left(x \right)} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2}} - \frac{2 \tan{\left(x \right)}}{x^{3}}}{\log{\left(x \right)}^{2} \tan^{2}{\left(x \right)} - 1}
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Gráfico
Derivada de y=arctanh(logtan(x))
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