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(x-sin(x))/(arcsin(x)-tg(x))
Derivada de la función/ (x-sin(x))/(arcsin(x)-tg(x))

Derivada de (x-sin(x))/(arcsin(x)-tg(x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   x - sin(x)   
----------------
asin(x) - tan(x)
x−sin⁡(x)−tan⁡(x)+asin⁡(x)\frac{x - \sin{\left(x \right)}}{- \tan{\left(x \right)} + \operatorname{asin}{\left(x \right)}} 
(x - sin(x))/(asin(x) - tan(x))
Gráfica
02468-8-6-4-2-10102.5-2.5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                /       2           1     \
                   (x - sin(x))*|1 + tan (x) - -----------|
                                |                 ________|
                                |                /      2 |
   1 - cos(x)                   \              \/  1 - x  /
---------------- + ----------------------------------------
asin(x) - tan(x)                               2           
                             (asin(x) - tan(x))
1−cos⁡(x)−tan⁡(x)+asin⁡(x)+(x−sin⁡(x))(tan⁡2(x)+1−11−x2)(−tan⁡(x)+asin⁡(x))2\frac{1 - \cos{\left(x \right)}}{- \tan{\left(x \right)} + \operatorname{asin}{\left(x \right)}} + \frac{\left(x - \sin{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\left(- \tan{\left(x \right)} + \operatorname{asin}{\left(x \right)}\right)^{2}}
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Segunda derivada [src] 
 /             /                                                                    2\                                                       \ 
 |             |                                         /       2           1     \ |                                                       | 
 |             |                                       2*|1 + tan (x) - -----------| |                                                       | 
 |             |                                         |                 ________| |                                                       | 
 |             |                                         |                /      2 | |                                                       | 
 |             |     x          /       2   \            \              \/  1 - x  / |                   /       2           1     \         | 
 |(x - sin(x))*|----------- - 2*\1 + tan (x)/*tan(x) + ------------------------------|   2*(-1 + cos(x))*|1 + tan (x) - -----------|         | 
 |             |        3/2                                  -asin(x) + tan(x)       |                   |                 ________|         | 
 |             |/     2\                                                             |                   |                /      2 |         | 
 |             \\1 - x /                                                             /                   \              \/  1 - x  /         | 
-|------------------------------------------------------------------------------------ + ------------------------------------------- + sin(x)| 
 \                                 -asin(x) + tan(x)                                                  -asin(x) + tan(x)                      / 
-----------------------------------------------------------------------------------------------------------------------------------------------
                                                               -asin(x) + tan(x)
−(x−sin⁡(x))(x(1−x2)32−2(tan⁡2(x)+1)tan⁡(x)+2(tan⁡2(x)+1−11−x2)2tan⁡(x)−asin⁡(x))tan⁡(x)−asin⁡(x)+2(cos⁡(x)−1)(tan⁡2(x)+1−11−x2)tan⁡(x)−asin⁡(x)+sin⁡(x)tan⁡(x)−asin⁡(x)- \frac{\frac{\left(x - \sin{\left(x \right)}\right) \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2}}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}}\right)}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}} + \frac{2 \left(\cos{\left(x \right)} - 1\right) \left(\tan^{2}{\left(x \right)} + 1 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}} + \sin{\left(x \right)}}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}}
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Tercera derivada [src] 
                       /                                                                                                        3                                                                       \                   /                                                                    2\                                       
                       |                                                                             /       2           1     \      /     x          /       2   \       \ /       2           1     \|                   |                                         /       2           1     \ |                                       
                       |                                                                           6*|1 + tan (x) - -----------|    6*|----------- - 2*\1 + tan (x)/*tan(x)|*|1 + tan (x) - -----------||                   |                                       2*|1 + tan (x) - -----------| |                                       
                       |                                                                             |                 ________|      |        3/2                         | |                 ________||                   |                                         |                 ________| |                                       
                       |                               2          2                                  |                /      2 |      |/     2\                            | |                /      2 ||                   |                                         |                /      2 | |                                       
                       |       1          /       2   \        3*x            2    /       2   \     \              \/  1 - x  /      \\1 - x /                            / \              \/  1 - x  /|                   |     x          /       2   \            \              \/  1 - x  / |     /       2           1     \       
          (x - sin(x))*|- ----------- + 2*\1 + tan (x)/  - ----------- + 4*tan (x)*\1 + tan (x)/ + ------------------------------ + --------------------------------------------------------------------|   3*(-1 + cos(x))*|----------- - 2*\1 + tan (x)/*tan(x) + ------------------------------|   3*|1 + tan (x) - -----------|*sin(x)
                       |          3/2                              5/2                                                     2                                 -asin(x) + tan(x)                          |                   |        3/2                                  -asin(x) + tan(x)       |     |                 ________|       
                       |  /     2\                         /     2\                                     (-asin(x) + tan(x))                                                                             |                   |/     2\                                                             |     |                /      2 |       
                       \  \1 - x /                         \1 - x /                                                                                                                                     /                   \\1 - x /                                                             /     \              \/  1 - x  /       
-cos(x) + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------- + ------------------------------------
                                                                                                 -asin(x) + tan(x)                                                                                                                             -asin(x) + tan(x)                                               -asin(x) + tan(x)          
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                            -asin(x) + tan(x)
(x−sin⁡(x))(−3x2(1−x2)52+6(x(1−x2)32−2(tan⁡2(x)+1)tan⁡(x))(tan⁡2(x)+1−11−x2)tan⁡(x)−asin⁡(x)+2(tan⁡2(x)+1)2+4(tan⁡2(x)+1)tan⁡2(x)+6(tan⁡2(x)+1−11−x2)3(tan⁡(x)−asin⁡(x))2−1(1−x2)32)tan⁡(x)−asin⁡(x)+3(cos⁡(x)−1)(x(1−x2)32−2(tan⁡2(x)+1)tan⁡(x)+2(tan⁡2(x)+1−11−x2)2tan⁡(x)−asin⁡(x))tan⁡(x)−asin⁡(x)−cos⁡(x)+3(tan⁡2(x)+1−11−x2)sin⁡(x)tan⁡(x)−asin⁡(x)tan⁡(x)−asin⁡(x)\frac{\frac{\left(x - \sin{\left(x \right)}\right) \left(- \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(\tan^{2}{\left(x \right)} + 1 - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\tan{\left(x \right)} - \operatorname{asin}{\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)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{3}}{\left(\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}\right)^{2}} - \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}} + \frac{3 \left(\cos{\left(x \right)} - 1\right) \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1 - \frac{1}{\sqrt{1 - x^{2}}}\right)^{2}}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}}\right)}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}} - \cos{\left(x \right)} + \frac{3 \left(\tan^{2}{\left(x \right)} + 1 - \frac{1}{\sqrt{1 - x^{2}}}\right) \sin{\left(x \right)}}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}}}{\tan{\left(x \right)} - \operatorname{asin}{\left(x \right)}}
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Gráfico
Derivada de (x-sin(x))/(arcsin(x)-tg(x))
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