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Derivada de (xsina-asinx)/(x-a)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
x*sin(a) - asin(x)
------------------
      x - a       
$$\frac{x \sin{\left(a \right)} - \operatorname{asin}{\left(x \right)}}{- a + x}$$
(x*sin(a) - asin(x))/(x - a)
Primera derivada [src]
       1                                   
- ----------- + sin(a)                     
     ________                              
    /      2                               
  \/  1 - x              x*sin(a) - asin(x)
---------------------- - ------------------
        x - a                        2     
                              (x - a)      
$$\frac{\sin{\left(a \right)} - \frac{1}{\sqrt{1 - x^{2}}}}{- a + x} - \frac{x \sin{\left(a \right)} - \operatorname{asin}{\left(x \right)}}{\left(- a + x\right)^{2}}$$
Segunda derivada [src]
                /       1              \                          
              2*|- ----------- + sin(a)|                          
                |     ________         |                          
                |    /      2          |                          
     x          \  \/  1 - x           /   2*(-asin(x) + x*sin(a))
----------- - -------------------------- - -----------------------
        3/2             a - x                             2       
/     2\                                           (a - x)        
\1 - x /                                                          
------------------------------------------------------------------
                              a - x                               
$$\frac{\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \left(\sin{\left(a \right)} - \frac{1}{\sqrt{1 - x^{2}}}\right)}{a - x} - \frac{2 \left(x \sin{\left(a \right)} - \operatorname{asin}{\left(x \right)}\right)}{\left(a - x\right)^{2}}}{a - x}$$
Tercera derivada [src]
            2                                /       1              \                      
         3*x                               6*|- ----------- + sin(a)|                      
  -1 + -------                               |     ________         |                      
             2                               |    /      2          |                      
       -1 + x    6*(-asin(x) + x*sin(a))     \  \/  1 - x           /           3*x        
- ------------ - ----------------------- - -------------------------- + -------------------
          3/2                   3                          2                    3/2        
  /     2\               (a - x)                    (a - x)             /     2\           
  \1 - x /                                                              \1 - x /   *(a - x)
-------------------------------------------------------------------------------------------
                                           a - x                                           
$$\frac{\frac{3 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \left(a - x\right)} - \frac{6 \left(\sin{\left(a \right)} - \frac{1}{\sqrt{1 - x^{2}}}\right)}{\left(a - x\right)^{2}} - \frac{6 \left(x \sin{\left(a \right)} - \operatorname{asin}{\left(x \right)}\right)}{\left(a - x\right)^{3}} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}}{a - x}$$