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y=ln((arccosx/x)+1)
Derivada de la función/ arccos/ cosx/x/ y=ln((arccosx/x)+1)

Derivada de y=ln((arccosx/x)+1)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   /acos(x)    \
log|------- + 1|
   \   x       /
log⁡(1+acos⁡(x)x)\log{\left(1 + \frac{\operatorname{acos}{\left(x \right)}}{x} \right)} 
log(acos(x)/x + 1)
Gráfica
02468-8-6-4-2-1010-2020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        1         acos(x)
- ------------- - -------
       ________       2  
      /      2       x   
  x*\/  1 - x            
-------------------------
       acos(x)           
       ------- + 1       
          x
−1x1−x2−acos⁡(x)x21+acos⁡(x)x\frac{- \frac{1}{x \sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{x^{2}}}{1 + \frac{\operatorname{acos}{\left(x \right)}}{x}}
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Segunda derivada [src] 
                                                                    2
                                             /     1        acos(x)\ 
                                             |----------- + -------| 
                                             |   ________      x   | 
                                             |  /      2           | 
       1        2*acos(x)         2          \\/  1 - x            / 
- ----------- + --------- + -------------- - ------------------------
          3/2        3            ________        2 /    acos(x)\    
  /     2\          x        2   /      2        x *|1 + -------|    
  \1 - x /                  x *\/  1 - x            \       x   /    
---------------------------------------------------------------------
                                 acos(x)                             
                             1 + -------                             
                                    x
−1(1−x2)32−(11−x2+acos⁡(x)x)2x2(1+acos⁡(x)x)+2x21−x2+2acos⁡(x)x31+acos⁡(x)x\frac{- \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\left(\frac{1}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x}\right)^{2}}{x^{2} \left(1 + \frac{\operatorname{acos}{\left(x \right)}}{x}\right)} + \frac{2}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{acos}{\left(x \right)}}{x^{3}}}{1 + \frac{\operatorname{acos}{\left(x \right)}}{x}}
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Tercera derivada [src] 
                                                                                      3                                                                         
                                                               /     1        acos(x)\      /     1        acos(x)\ /       1        2*acos(x)         2       \
                                                             2*|----------- + -------|    3*|----------- + -------|*|- ----------- + --------- + --------------|
                                                               |   ________      x   |      |   ________      x   | |          3/2        3            ________|
                                                               |  /      2           |      |  /      2           | |  /     2\          x        2   /      2 |
  6*acos(x)         6              3*x             2           \\/  1 - x            /      \\/  1 - x            / \  \1 - x /                  x *\/  1 - x  /
- --------- - -------------- - ----------- + ------------- - -------------------------- + ----------------------------------------------------------------------
       4            ________           5/2             3/2                       2                                     /    acos(x)\                            
      x        3   /      2    /     2\        /     2\           3 /    acos(x)\                                    x*|1 + -------|                            
              x *\/  1 - x     \1 - x /      x*\1 - x /          x *|1 + -------|                                      \       x   /                            
                                                                    \       x   /                                                                               
----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                              acos(x)                                                                           
                                                                          1 + -------                                                                           
                                                                                 x
−3x(1−x2)52+3(11−x2+acos⁡(x)x)(−1(1−x2)32+2x21−x2+2acos⁡(x)x3)x(1+acos⁡(x)x)+2x(1−x2)32−2(11−x2+acos⁡(x)x)3x3(1+acos⁡(x)x)2−6x31−x2−6acos⁡(x)x41+acos⁡(x)x\frac{- \frac{3 x}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 \left(\frac{1}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x}\right) \left(- \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2}{x^{2} \sqrt{1 - x^{2}}} + \frac{2 \operatorname{acos}{\left(x \right)}}{x^{3}}\right)}{x \left(1 + \frac{\operatorname{acos}{\left(x \right)}}{x}\right)} + \frac{2}{x \left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 \left(\frac{1}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x}\right)^{3}}{x^{3} \left(1 + \frac{\operatorname{acos}{\left(x \right)}}{x}\right)^{2}} - \frac{6}{x^{3} \sqrt{1 - x^{2}}} - \frac{6 \operatorname{acos}{\left(x \right)}}{x^{4}}}{1 + \frac{\operatorname{acos}{\left(x \right)}}{x}}
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Gráfico
Derivada de y=ln((arccosx/x)+1)
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