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(x^tgx)/(1+arcsinx)
Derivada de la función/ x^tgx/ arcsin/ (x^tgx)/(1+arcsinx)

Derivada de (x^tgx)/(1+arcsinx)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   tan(x)  
  x        
-----------
1 + asin(x)
xtan⁡(x)asin⁡(x)+1\frac{x^{\tan{\left(x \right)}}}{\operatorname{asin}{\left(x \right)} + 1} 
x^tan(x)/(1 + asin(x))
Gráfica
02468-8-6-4-2-10102.5-2.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 tan(x) /tan(x)   /       2   \       \                             
x      *|------ + \1 + tan (x)/*log(x)|             tan(x)          
        \  x                          /            x                
--------------------------------------- - --------------------------
              1 + asin(x)                    ________               
                                            /      2               2
                                          \/  1 - x  *(1 + asin(x))
xtan⁡(x)((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)asin⁡(x)+1−xtan⁡(x)1−x2(asin⁡(x)+1)2\frac{x^{\tan{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)}{\operatorname{asin}{\left(x \right)} + 1} - \frac{x^{\tan{\left(x \right)}}}{\sqrt{1 - x^{2}} \left(\operatorname{asin}{\left(x \right)} + 1\right)^{2}}
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Segunda derivada [src] 
        /                                                 x                   2                                                                                                 \
        |                                            ----------- + -----------------------                                                                                      |
        |                                                    3/2                 /      2\                       /tan(x)   /       2   \       \                                |
        |                               2            /     2\      (1 + asin(x))*\-1 + x /     /       2   \   2*|------ + \1 + tan (x)/*log(x)|                                |
 tan(x) |/tan(x)   /       2   \       \    tan(x)   \1 - x /                                2*\1 + tan (x)/     \  x                          /     /       2   \              |
x      *||------ + \1 + tan (x)/*log(x)|  - ------ - ------------------------------------- + --------------- - --------------------------------- + 2*\1 + tan (x)/*log(x)*tan(x)|
        |\  x                          /       2                  1 + asin(x)                       x                 ________                                                  |
        |                                     x                                                                      /      2                                                   |
        \                                                                                                          \/  1 - x  *(1 + asin(x))                                    /
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                   1 + asin(x)
xtan⁡(x)(−x(1−x2)32+2(x2−1)(asin⁡(x)+1)asin⁡(x)+1+((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)−2((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)1−x2(asin⁡(x)+1)+2(tan⁡2(x)+1)x−tan⁡(x)x2)asin⁡(x)+1\frac{x^{\tan{\left(x \right)}} \left(- \frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(x^{2} - 1\right) \left(\operatorname{asin}{\left(x \right)} + 1\right)}}{\operatorname{asin}{\left(x \right)} + 1} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} - \frac{2 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)}{\sqrt{1 - x^{2}} \left(\operatorname{asin}{\left(x \right)} + 1\right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{\tan{\left(x \right)}}{x^{2}}\right)}{\operatorname{asin}{\left(x \right)} + 1}
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3-я производная [src] 
        /                                                        2                                                                                                                                                                                                                                                                                                                                                                                                                                                           \
        |                                        1            3*x                   6                          6*x                                                                                                                                                                        /                               2              /       2   \                                \     /     x                   2           \ /tan(x)   /       2   \       \                                                          |
        |                                   ----------- + ----------- + -------------------------- - ------------------------                                                                                                                                                             |/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              |   3*|----------- + -----------------------|*|------ + \1 + tan (x)/*log(x)|                                                          |
        |                                           3/2           5/2           3/2                                         2                                                                                                                                                           3*||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|     |        3/2                 /      2\| \  x                          /                                                          |
        |                               3   /     2\      /     2\      /     2\                 2                 /      2\      /       2   \                             2                                            /             /       2   \                                \     |\  x                          /       2            x                                       |     |/     2\      (1 + asin(x))*\-1 + x /|                                                                      /       2   \       |
 tan(x) |/tan(x)   /       2   \       \    \1 - x /      \1 - x /      \1 - x /   *(1 + asin(x))    (1 + asin(x))*\-1 + x /    3*\1 + tan (x)/   2*tan(x)     /       2   \             /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |     \                                     x                                                     /     \\1 - x /                             /                                        2    /       2   \          6*\1 + tan (x)/*tan(x)|
x      *||------ + \1 + tan (x)/*log(x)|  - --------------------------------------------------------------------------------- - --------------- + -------- + 2*\1 + tan (x)/ *log(x) + 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| - ----------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------- + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------|
        |\  x                          /                                       1 + asin(x)                                              2             3                                  \  x                          / |     2            x                                       |                                         ________                                                                                   1 + asin(x)                                                                             x           |
        |                                                                                                                              x             x                                                                   \    x                                                     /                                        /      2                                                                                                                                                                                        |
        \                                                                                                                                                                                                                                                                                                                  \/  1 - x  *(1 + asin(x))                                                                                                                                                                         /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                         1 + asin(x)
xtan⁡(x)(−3(x(1−x2)32+2(x2−1)(asin⁡(x)+1))((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)asin⁡(x)+1+((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)3+3((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)+2(tan⁡2(x)+1)2log⁡(x)+4(tan⁡2(x)+1)log⁡(x)tan⁡2(x)−3x2(1−x2)52−6x(x2−1)2(asin⁡(x)+1)+1(1−x2)32+6(1−x2)32(asin⁡(x)+1)2asin⁡(x)+1−3(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)1−x2(asin⁡(x)+1)+6(tan⁡2(x)+1)tan⁡(x)x−3(tan⁡2(x)+1)x2+2tan⁡(x)x3)asin⁡(x)+1\frac{x^{\tan{\left(x \right)}} \left(- \frac{3 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(x^{2} - 1\right) \left(\operatorname{asin}{\left(x \right)} + 1\right)}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)}{\operatorname{asin}{\left(x \right)} + 1} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 \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) + 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{\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x}{\left(x^{2} - 1\right)^{2} \left(\operatorname{asin}{\left(x \right)} + 1\right)} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\operatorname{asin}{\left(x \right)} + 1\right)^{2}}}{\operatorname{asin}{\left(x \right)} + 1} - \frac{3 \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 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)}{\sqrt{1 - x^{2}} \left(\operatorname{asin}{\left(x \right)} + 1\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}}\right)}{\operatorname{asin}{\left(x \right)} + 1}
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Tercera derivada [src] 
        /                                                        2                                                                                                                                                                                                                                                                                                                                                                                                                                                           \
        |                                        1            3*x                   6                          6*x                                                                                                                                                                        /                               2              /       2   \                                \     /     x                   2           \ /tan(x)   /       2   \       \                                                          |
        |                                   ----------- + ----------- + -------------------------- - ------------------------                                                                                                                                                             |/tan(x)   /       2   \       \    tan(x)   2*\1 + tan (x)/     /       2   \              |   3*|----------- + -----------------------|*|------ + \1 + tan (x)/*log(x)|                                                          |
        |                                           3/2           5/2           3/2                                         2                                                                                                                                                           3*||------ + \1 + tan (x)/*log(x)|  - ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)|     |        3/2                 /      2\| \  x                          /                                                          |
        |                               3   /     2\      /     2\      /     2\                 2                 /      2\      /       2   \                             2                                            /             /       2   \                                \     |\  x                          /       2            x                                       |     |/     2\      (1 + asin(x))*\-1 + x /|                                                                      /       2   \       |
 tan(x) |/tan(x)   /       2   \       \    \1 - x /      \1 - x /      \1 - x /   *(1 + asin(x))    (1 + asin(x))*\-1 + x /    3*\1 + tan (x)/   2*tan(x)     /       2   \             /tan(x)   /       2   \       \ |  tan(x)   2*\1 + tan (x)/     /       2   \              |     \                                     x                                                     /     \\1 - x /                             /                                        2    /       2   \          6*\1 + tan (x)/*tan(x)|
x      *||------ + \1 + tan (x)/*log(x)|  - --------------------------------------------------------------------------------- - --------------- + -------- + 2*\1 + tan (x)/ *log(x) + 3*|------ + \1 + tan (x)/*log(x)|*|- ------ + --------------- + 2*\1 + tan (x)/*log(x)*tan(x)| - ----------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------- + 4*tan (x)*\1 + tan (x)/*log(x) + ----------------------|
        |\  x                          /                                       1 + asin(x)                                              2             3                                  \  x                          / |     2            x                                       |                                         ________                                                                                   1 + asin(x)                                                                             x           |
        |                                                                                                                              x             x                                                                   \    x                                                     /                                        /      2                                                                                                                                                                                        |
        \                                                                                                                                                                                                                                                                                                                  \/  1 - x  *(1 + asin(x))                                                                                                                                                                         /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                         1 + asin(x)
xtan⁡(x)(−3(x(1−x2)32+2(x2−1)(asin⁡(x)+1))((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)asin⁡(x)+1+((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)3+3((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)+2(tan⁡2(x)+1)2log⁡(x)+4(tan⁡2(x)+1)log⁡(x)tan⁡2(x)−3x2(1−x2)52−6x(x2−1)2(asin⁡(x)+1)+1(1−x2)32+6(1−x2)32(asin⁡(x)+1)2asin⁡(x)+1−3(((tan⁡2(x)+1)log⁡(x)+tan⁡(x)x)2+2(tan⁡2(x)+1)log⁡(x)tan⁡(x)+2(tan⁡2(x)+1)x−tan⁡(x)x2)1−x2(asin⁡(x)+1)+6(tan⁡2(x)+1)tan⁡(x)x−3(tan⁡2(x)+1)x2+2tan⁡(x)x3)asin⁡(x)+1\frac{x^{\tan{\left(x \right)}} \left(- \frac{3 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(x^{2} - 1\right) \left(\operatorname{asin}{\left(x \right)} + 1\right)}\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)}{\operatorname{asin}{\left(x \right)} + 1} + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{3} + 3 \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) + 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{\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{6 x}{\left(x^{2} - 1\right)^{2} \left(\operatorname{asin}{\left(x \right)} + 1\right)} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(\operatorname{asin}{\left(x \right)} + 1\right)^{2}}}{\operatorname{asin}{\left(x \right)} + 1} - \frac{3 \left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} + \frac{\tan{\left(x \right)}}{x}\right)^{2} + 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)}{\sqrt{1 - x^{2}} \left(\operatorname{asin}{\left(x \right)} + 1\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}}\right)}{\operatorname{asin}{\left(x \right)} + 1}
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Gráfico
Derivada de (x^tgx)/(1+arcsinx)
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