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y=arccos(ln^5x)
Derivada de la función/ ln^5x/ arccos/ y=arccos(ln^5x)

Derivada de y=arccos(ln^5x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
    /   5   \
acos\log (x)/
acos⁡(log⁡(x)5)\operatorname{acos}{\left(\log{\left(x \right)}^{5} \right)} 
acos(log(x)^5)
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
           4       
     -5*log (x)    
-------------------
     ______________
    /        10    
x*\/  1 - log  (x)
−5log⁡(x)4x1−log⁡(x)10- \frac{5 \log{\left(x \right)}^{4}}{x \sqrt{1 - \log{\left(x \right)}^{10}}}
Simplificar
Segunda derivada [src] 
          /           10             \
     3    |      5*log  (x)          |
5*log (x)*|-4 - ------------ + log(x)|
          |            10            |
          \     1 - log  (x)         /
--------------------------------------
               ______________         
          2   /        10             
         x *\/  1 - log  (x)
5(log⁡(x)−4−5log⁡(x)101−log⁡(x)10)log⁡(x)3x21−log⁡(x)10\frac{5 \left(\log{\left(x \right)} - 4 - \frac{5 \log{\left(x \right)}^{10}}{1 - \log{\left(x \right)}^{10}}\right) \log{\left(x \right)}^{3}}{x^{2} \sqrt{1 - \log{\left(x \right)}^{10}}}
Simplificar
Tercera derivada [src] 
          /                                    10               20              11    \
     2    |           2                  85*log  (x)      75*log  (x)     15*log  (x) |
5*log (x)*|-12 - 2*log (x) + 12*log(x) - ------------ - --------------- + ------------|
          |                                     10                    2          10   |
          |                              1 - log  (x)   /       10   \    1 - log  (x)|
          \                                             \1 - log  (x)/                /
---------------------------------------------------------------------------------------
                                        ______________                                 
                                   3   /        10                                     
                                  x *\/  1 - log  (x)
5(−2log⁡(x)2+12log⁡(x)−12+15log⁡(x)111−log⁡(x)10−85log⁡(x)101−log⁡(x)10−75log⁡(x)20(1−log⁡(x)10)2)log⁡(x)2x31−log⁡(x)10\frac{5 \left(- 2 \log{\left(x \right)}^{2} + 12 \log{\left(x \right)} - 12 + \frac{15 \log{\left(x \right)}^{11}}{1 - \log{\left(x \right)}^{10}} - \frac{85 \log{\left(x \right)}^{10}}{1 - \log{\left(x \right)}^{10}} - \frac{75 \log{\left(x \right)}^{20}}{\left(1 - \log{\left(x \right)}^{10}\right)^{2}}\right) \log{\left(x \right)}^{2}}{x^{3} \sqrt{1 - \log{\left(x \right)}^{10}}}
Simplificar
Gráfico
Derivada de y=arccos(ln^5x)
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