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Derivada de la función/ arccos/ y=lncos/ y=lncose^arccosx

Derivada de y=lncose^arccosx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   acos(x)        
log       (cos(E))
$$\log{\left(\cos{\left(e \right)} \right)}^{\operatorname{acos}{\left(x \right)}}$$ 
log(cos(E))^acos(x)
Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
    acos(x)                          
-log       (cos(E))*log(log(cos(E))) 
-------------------------------------
                ________             
               /      2              
             \/  1 - x
$$- \frac{\log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)} \log{\left(\cos{\left(e \right)} \right)}^{\operatorname{acos}{\left(x \right)}}}{\sqrt{1 - x^{2}}}$$
Simplificar
Segunda derivada [src] 
    acos(x)         /     x        log(log(cos(E)))\                 
-log       (cos(E))*|----------- + ----------------|*log(log(cos(E)))
                    |        3/2             2     |                 
                    |/     2\          -1 + x      |                 
                    \\1 - x /                      /
$$- \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)}}{x^{2} - 1}\right) \log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)} \log{\left(\cos{\left(e \right)} \right)}^{\operatorname{acos}{\left(x \right)}}$$
Simplificar
Tercera derivada [src] 
                   /                   2                       2                          \                 
   acos(x)         |       1        log (log(cos(E)))       3*x       3*x*log(log(cos(E)))|                 
log       (cos(E))*|- ----------- - ----------------- - ----------- + --------------------|*log(log(cos(E)))
                   |          3/2              3/2              5/2                 2     |                 
                   |  /     2\         /     2\         /     2\           /      2\      |                 
                   \  \1 - x /         \1 - x /         \1 - x /           \-1 + x /      /
$$\left(- \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x \log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)} \log{\left(\cos{\left(e \right)} \right)}^{\operatorname{acos}{\left(x \right)}}$$
Simplificar
3-я производная [src] 
                   /                   2                       2                          \                 
   acos(x)         |       1        log (log(cos(E)))       3*x       3*x*log(log(cos(E)))|                 
log       (cos(E))*|- ----------- - ----------------- - ----------- + --------------------|*log(log(cos(E)))
                   |          3/2              3/2              5/2                 2     |                 
                   |  /     2\         /     2\         /     2\           /      2\      |                 
                   \  \1 - x /         \1 - x /         \1 - x /           \-1 + x /      /
$$\left(- \frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x \log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)}^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right) \log{\left(\log{\left(\cos{\left(e \right)} \right)} \right)} \log{\left(\cos{\left(e \right)} \right)}^{\operatorname{acos}{\left(x \right)}}$$
Simplificar
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