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(x*sqrt(1+sin(x))+ln(1-x))/(tg(x)-sin(x))
Derivada de la función/ (x*sqrt(1+sin(x))+ln(1-x))/(tg(x)-sin(x))

Derivada de (x*sqrt(1+sin(x))+ln(1-x))/(tg(x)-sin(x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
    ____________             
x*\/ 1 + sin(x)  + log(1 - x)
-----------------------------
       tan(x) - sin(x)
xsin⁡(x)+1+log⁡(1−x)−sin⁡(x)+tan⁡(x)\frac{x \sqrt{\sin{\left(x \right)} + 1} + \log{\left(1 - x \right)}}{- \sin{\left(x \right)} + \tan{\left(x \right)}} 
(x*sqrt(1 + sin(x)) + log(1 - x))/(tan(x) - sin(x))
Gráfica
02468-8-6-4-2-1010-5000001000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  ____________     1         x*cos(x)                                                              
\/ 1 + sin(x)  - ----- + ----------------                                                          
                 1 - x       ____________   /    ____________             \ /        2            \
                         2*\/ 1 + sin(x)    \x*\/ 1 + sin(x)  + log(1 - x)/*\-1 - tan (x) + cos(x)/
----------------------------------------- + -------------------------------------------------------
             tan(x) - sin(x)                                                    2                  
                                                               (tan(x) - sin(x))
(xsin⁡(x)+1+log⁡(1−x))(cos⁡(x)−tan⁡2(x)−1)(−sin⁡(x)+tan⁡(x))2+xcos⁡(x)2sin⁡(x)+1+sin⁡(x)+1−11−x−sin⁡(x)+tan⁡(x)\frac{\left(x \sqrt{\sin{\left(x \right)} + 1} + \log{\left(1 - x \right)}\right) \left(\cos{\left(x \right)} - \tan^{2}{\left(x \right)} - 1\right)}{\left(- \sin{\left(x \right)} + \tan{\left(x \right)}\right)^{2}} + \frac{\frac{x \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}} + \sqrt{\sin{\left(x \right)} + 1} - \frac{1}{1 - x}}{- \sin{\left(x \right)} + \tan{\left(x \right)}}
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Segunda derivada [src] 
                                                                                /                        2                                  \                                                                                          
                                                                                |  /       2            \                                   |   /       2            \ /    ____________     2         x*cos(x)   \                    
                                                /    ____________             \ |2*\1 + tan (x) - cos(x)/      /       2   \                |   \1 + tan (x) - cos(x)/*|2*\/ 1 + sin(x)  + ------ + --------------|                    
                                                \x*\/ 1 + sin(x)  + log(1 - x)/*|------------------------- + 2*\1 + tan (x)/*tan(x) + sin(x)|                          |                   -1 + x     ____________|            2       
    1           cos(x)           x*sin(x)                                       \     -tan(x) + sin(x)                                      /                          \                            \/ 1 + sin(x) /       x*cos (x)    
--------- - -------------- + ---------------- - --------------------------------------------------------------------------------------------- - ------------------------------------------------------------------- + -----------------
        2     ____________       ____________                                          -tan(x) + sin(x)                                                                   -tan(x) + sin(x)                                          3/2
(-1 + x)    \/ 1 + sin(x)    2*\/ 1 + sin(x)                                                                                                                                                                          4*(1 + sin(x))   
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                            -tan(x) + sin(x)
xsin⁡(x)2sin⁡(x)+1+xcos⁡2(x)4(sin⁡(x)+1)32−(xsin⁡(x)+1+log⁡(1−x))(2(tan⁡2(x)+1)tan⁡(x)+sin⁡(x)+2(−cos⁡(x)+tan⁡2(x)+1)2sin⁡(x)−tan⁡(x))sin⁡(x)−tan⁡(x)−(xcos⁡(x)sin⁡(x)+1+2sin⁡(x)+1+2x−1)(−cos⁡(x)+tan⁡2(x)+1)sin⁡(x)−tan⁡(x)−cos⁡(x)sin⁡(x)+1+1(x−1)2sin⁡(x)−tan⁡(x)\frac{\frac{x \sin{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}} + \frac{x \cos^{2}{\left(x \right)}}{4 \left(\sin{\left(x \right)} + 1\right)^{\frac{3}{2}}} - \frac{\left(x \sqrt{\sin{\left(x \right)} + 1} + \log{\left(1 - x \right)}\right) \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \sin{\left(x \right)} + \frac{2 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)^{2}}{\sin{\left(x \right)} - \tan{\left(x \right)}}\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} - \frac{\left(\frac{x \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)} + 1}} + 2 \sqrt{\sin{\left(x \right)} + 1} + \frac{2}{x - 1}\right) \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} - \frac{\cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)} + 1}} + \frac{1}{\left(x - 1\right)^{2}}}{\sin{\left(x \right)} - \tan{\left(x \right)}}
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Tercera derivada [src] 
                                                                                                        /                                                                     3                                                                      \                                                  /                        2                                  \                                                                                                                                   
                                                                                                        |               2                               /       2            \      /  /       2   \                \ /       2            \         |                                                  |  /       2            \                                   |                                                /                                     2                       \                    
                                                                        /    ____________             \ |  /       2   \         2    /       2   \   6*\1 + tan (x) - cos(x)/    6*\2*\1 + tan (x)/*tan(x) + sin(x)/*\1 + tan (x) - cos(x)/         |     /    ____________     2         x*cos(x)   \ |2*\1 + tan (x) - cos(x)/      /       2   \                |                         /       2            \ |    4          4*cos(x)         x*cos (x)        2*x*sin(x)  |                    
                                                                        \x*\/ 1 + sin(x)  + log(1 - x)/*|2*\1 + tan (x)/  + 4*tan (x)*\1 + tan (x)/ + ------------------------- + ---------------------------------------------------------- + cos(x)|   3*|2*\/ 1 + sin(x)  + ------ + --------------|*|------------------------- + 2*\1 + tan (x)/*tan(x) + sin(x)|                       3*\1 + tan (x) - cos(x)/*|--------- - -------------- + --------------- + --------------|                    
                                          2                                                             |                                                                  2                           -tan(x) + sin(x)                              |     |                   -1 + x     ____________| \     -tan(x) + sin(x)                                      /             3                                  |        2     ____________               3/2     ____________|                    
      2           3*sin(x)           3*cos (x)           x*cos(x)                                       \                                                (-tan(x) + sin(x))                                                                          /     \                            \/ 1 + sin(x) /                                                                    3*x*cos (x)                               \(-1 + x)    \/ 1 + sin(x)    (1 + sin(x))      \/ 1 + sin(x) /   3*x*cos(x)*sin(x)
- --------- + ---------------- + ----------------- + ---------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------ - ----------------- + ---------------------------------------------------------------------------------------- - -----------------
          3       ____________                 3/2       ____________                                                                                  -tan(x) + sin(x)                                                                                                                              2*(-tan(x) + sin(x))                                                             5/2                                     4*(-tan(x) + sin(x))                                                   3/2
  (-1 + x)    2*\/ 1 + sin(x)    4*(1 + sin(x))      2*\/ 1 + sin(x)                                                                                                                                                                                                                                                                                                    8*(1 + sin(x))                                                                                                 4*(1 + sin(x))   
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                            -tan(x) + sin(x)
xcos⁡(x)2sin⁡(x)+1−3xsin⁡(x)cos⁡(x)4(sin⁡(x)+1)32−3xcos⁡3(x)8(sin⁡(x)+1)52−(xsin⁡(x)+1+log⁡(1−x))(6(2(tan⁡2(x)+1)tan⁡(x)+sin⁡(x))(−cos⁡(x)+tan⁡2(x)+1)sin⁡(x)−tan⁡(x)+2(tan⁡2(x)+1)2+4(tan⁡2(x)+1)tan⁡2(x)+cos⁡(x)+6(−cos⁡(x)+tan⁡2(x)+1)3(sin⁡(x)−tan⁡(x))2)sin⁡(x)−tan⁡(x)−3(2(tan⁡2(x)+1)tan⁡(x)+sin⁡(x)+2(−cos⁡(x)+tan⁡2(x)+1)2sin⁡(x)−tan⁡(x))(xcos⁡(x)sin⁡(x)+1+2sin⁡(x)+1+2x−1)2(sin⁡(x)−tan⁡(x))+3(−cos⁡(x)+tan⁡2(x)+1)(2xsin⁡(x)sin⁡(x)+1+xcos⁡2(x)(sin⁡(x)+1)32−4cos⁡(x)sin⁡(x)+1+4(x−1)2)4(sin⁡(x)−tan⁡(x))+3sin⁡(x)2sin⁡(x)+1+3cos⁡2(x)4(sin⁡(x)+1)32−2(x−1)3sin⁡(x)−tan⁡(x)\frac{\frac{x \cos{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}} - \frac{3 x \sin{\left(x \right)} \cos{\left(x \right)}}{4 \left(\sin{\left(x \right)} + 1\right)^{\frac{3}{2}}} - \frac{3 x \cos^{3}{\left(x \right)}}{8 \left(\sin{\left(x \right)} + 1\right)^{\frac{5}{2}}} - \frac{\left(x \sqrt{\sin{\left(x \right)} + 1} + \log{\left(1 - x \right)}\right) \left(\frac{6 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \sin{\left(x \right)}\right) \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \cos{\left(x \right)} + \frac{6 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)^{3}}{\left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)^{2}}\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} - \frac{3 \left(2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \sin{\left(x \right)} + \frac{2 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)^{2}}{\sin{\left(x \right)} - \tan{\left(x \right)}}\right) \left(\frac{x \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)} + 1}} + 2 \sqrt{\sin{\left(x \right)} + 1} + \frac{2}{x - 1}\right)}{2 \left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)} + \frac{3 \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right) \left(\frac{2 x \sin{\left(x \right)}}{\sqrt{\sin{\left(x \right)} + 1}} + \frac{x \cos^{2}{\left(x \right)}}{\left(\sin{\left(x \right)} + 1\right)^{\frac{3}{2}}} - \frac{4 \cos{\left(x \right)}}{\sqrt{\sin{\left(x \right)} + 1}} + \frac{4}{\left(x - 1\right)^{2}}\right)}{4 \left(\sin{\left(x \right)} - \tan{\left(x \right)}\right)} + \frac{3 \sin{\left(x \right)}}{2 \sqrt{\sin{\left(x \right)} + 1}} + \frac{3 \cos^{2}{\left(x \right)}}{4 \left(\sin{\left(x \right)} + 1\right)^{\frac{3}{2}}} - \frac{2}{\left(x - 1\right)^{3}}}{\sin{\left(x \right)} - \tan{\left(x \right)}}
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Gráfico
Derivada de (x*sqrt(1+sin(x))+ln(1-x))/(tg(x)-sin(x))
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