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y=(arctg*x-arcsin*x)/(tg*x-sin*x)
Derivada de la función/ y=(arctg*x-arcsin*x)/(tg*x-sin*x)

Derivada de y=(arctg*x-arcsin*x)/(tg*x-sin*x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
atan(x) - asin(x)
-----------------
 tan(x) - sin(x)
−asin⁡(x)+atan⁡(x)−sin⁡(x)+tan⁡(x)\frac{- \operatorname{asin}{\left(x \right)} + \operatorname{atan}{\left(x \right)}}{- \sin{\left(x \right)} + \tan{\left(x \right)}} 
(atan(x) - asin(x))/(tan(x) - sin(x))
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
  1           1                                                   
------ - -----------                                              
     2      ________                                              
1 + x      /      2                        /        2            \
         \/  1 - x     (atan(x) - asin(x))*\-1 - tan (x) + cos(x)/
-------------------- + -------------------------------------------
  tan(x) - sin(x)                                    2            
                                    (tan(x) - sin(x))
1x2+1−11−x2−sin⁡(x)+tan⁡(x)+(−asin⁡(x)+atan⁡(x))(cos⁡(x)−tan⁡2(x)−1)(−sin⁡(x)+tan⁡(x))2\frac{\frac{1}{x^{2} + 1} - \frac{1}{\sqrt{1 - x^{2}}}}{- \sin{\left(x \right)} + \tan{\left(x \right)}} + \frac{\left(- \operatorname{asin}{\left(x \right)} + \operatorname{atan}{\left(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}}
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Segunda derivada [src] 
                                                   /                        2                                  \     /  1           1     \ /       2            \
                                                   |  /       2            \                                   |   2*|------ - -----------|*\1 + tan (x) - cos(x)/
                                                   |2*\1 + tan (x) - cos(x)/      /       2   \                |     |     2      ________|                       
                              (-atan(x) + asin(x))*|------------------------- + 2*\1 + tan (x)/*tan(x) + sin(x)|     |1 + x      /      2 |                       
  /     1            2    \                        \     -tan(x) + sin(x)                                      /     \         \/  1 - x  /                       
x*|----------- + ---------| + ---------------------------------------------------------------------------------- - -----------------------------------------------
  |        3/2           2|                                    -tan(x) + sin(x)                                                    -tan(x) + sin(x)               
  |/     2\      /     2\ |                                                                                                                                       
  \\1 - x /      \1 + x / /                                                                                                                                       
------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                         -tan(x) + sin(x)
x(2(x2+1)2+1(1−x2)32)−2(1x2+1−11−x2)(−cos⁡(x)+tan⁡2(x)+1)sin⁡(x)−tan⁡(x)+(asin⁡(x)−atan⁡(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)sin⁡(x)−tan⁡(x)\frac{x \left(\frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) - \frac{2 \left(\frac{1}{x^{2} + 1} - \frac{1}{\sqrt{1 - x^{2}}}\right) \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} + \frac{\left(\operatorname{asin}{\left(x \right)} - \operatorname{atan}{\left(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)}}}{\sin{\left(x \right)} - \tan{\left(x \right)}}
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Tercera derivada [src] 
                                                                                                                                                                                                                                                   /                        2                                  \                                                       
                                                                         /                                                                     3                                                                      \                            |  /       2            \                                   |                                                       
                                                                         |               2                               /       2            \      /  /       2   \                \ /       2            \         |     /  1           1     \ |2*\1 + tan (x) - cos(x)/      /       2   \                |       /     1            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)/         |   3*|------ - -----------|*|------------------------- + 2*\1 + tan (x)/*tan(x) + sin(x)|   3*x*|----------- + ---------|*\1 + tan (x) - cos(x)/
                                                    (-atan(x) + asin(x))*|2*\1 + tan (x)/  + 4*tan (x)*\1 + tan (x)/ + ------------------------- + ---------------------------------------------------------- + cos(x)|     |     2      ________| \     -tan(x) + sin(x)                                      /       |        3/2           2|                       
                                2            2                           |                                                                  2                           -tan(x) + sin(x)                              |     |1 + x      /      2 |                                                                     |/     2\      /     2\ |                       
     1            2          8*x          3*x                            \                                                (-tan(x) + sin(x))                                                                          /     \         \/  1 - x  /                                                                     \\1 - x /      \1 + x / /                       
----------- + --------- - --------- + ----------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------- + ----------------------------------------------------
        3/2           2           3           5/2                                                                             -tan(x) + sin(x)                                                                                                               -tan(x) + sin(x)                                                        -tan(x) + sin(x)                  
/     2\      /     2\    /     2\    /     2\                                                                                                                                                                                                                                                                                                                         
\1 - x /      \1 + x /    \1 + x /    \1 - x /                                                                                                                                                                                                                                                                                                                         
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                            -tan(x) + sin(x)
−8x2(x2+1)3+3x2(1−x2)52+3x(2(x2+1)2+1(1−x2)32)(−cos⁡(x)+tan⁡2(x)+1)sin⁡(x)−tan⁡(x)−3(1x2+1−11−x2)(2(tan⁡2(x)+1)tan⁡(x)+sin⁡(x)+2(−cos⁡(x)+tan⁡2(x)+1)2sin⁡(x)−tan⁡(x))sin⁡(x)−tan⁡(x)+(asin⁡(x)−atan⁡(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)+2(x2+1)2+1(1−x2)32sin⁡(x)−tan⁡(x)\frac{- \frac{8 x^{2}}{\left(x^{2} + 1\right)^{3}} + \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x \left(\frac{2}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \left(- \cos{\left(x \right)} + \tan^{2}{\left(x \right)} + 1\right)}{\sin{\left(x \right)} - \tan{\left(x \right)}} - \frac{3 \left(\frac{1}{x^{2} + 1} - \frac{1}{\sqrt{1 - x^{2}}}\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(\operatorname{asin}{\left(x \right)} - \operatorname{atan}{\left(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{2}{\left(x^{2} + 1\right)^{2}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{\sin{\left(x \right)} - \tan{\left(x \right)}}
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Gráfico
Derivada de y=(arctg*x-arcsin*x)/(tg*x-sin*x)
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