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Derivada de y=ctg2e^x-(x*arccos3x)/3-lnx

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

Ha introducido [src]
   x        x*acos(3*x)         
cot (2*E) - ----------- - log(x)
                 3              
$$\left(- \frac{x \operatorname{acos}{\left(3 x \right)}}{3} + \cot^{x}{\left(2 e \right)}\right) - \log{\left(x \right)}$$
cot(2*E)^x - x*acos(3*x)/3 - log(x)
Primera derivada [src]
  1   acos(3*x)         x            x                   
- - - --------- + ------------- + cot (2*E)*log(cot(2*E))
  x       3          __________                          
                    /        2                           
                  \/  1 - 9*x                            
$$\frac{x}{\sqrt{1 - 9 x^{2}}} + \log{\left(\cot{\left(2 e \right)} \right)} \cot^{x}{\left(2 e \right)} - \frac{\operatorname{acos}{\left(3 x \right)}}{3} - \frac{1}{x}$$
Segunda derivada [src]
                                                        2    
1          2            x         2                  9*x     
-- + ------------- + cot (2*E)*log (cot(2*E)) + -------------
 2      __________                                        3/2
x      /        2                               /       2\   
     \/  1 - 9*x                                \1 - 9*x /   
$$\frac{9 x^{2}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \log{\left(\cot{\left(2 e \right)} \right)}^{2} \cot^{x}{\left(2 e \right)} + \frac{2}{\sqrt{1 - 9 x^{2}}} + \frac{1}{x^{2}}$$
Tercera derivada [src]
                                                           3   
  2       x         3                  36*x           243*x    
- -- + cot (2*E)*log (cot(2*E)) + ------------- + -------------
   3                                        3/2             5/2
  x                               /       2\      /       2\   
                                  \1 - 9*x /      \1 - 9*x /   
$$\frac{243 x^{3}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} + \frac{36 x}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \log{\left(\cot{\left(2 e \right)} \right)}^{3} \cot^{x}{\left(2 e \right)} - \frac{2}{x^{3}}$$