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y=arcctg(ctg^2(x))
Derivada de la función/ tg^2(x)/ ctg^2/ y=arcctg(ctg^2(x))

Derivada de y=arcctg(ctg^2(x))

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

Gráfico:

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Solución

Ha introducido [src] 
    /   2   \
acot\cot (x)/
acot⁡(cot⁡2(x))\operatorname{acot}{\left(\cot^{2}{\left(x \right)} \right)} 
acot(cot(x)^2)
Gráfica
02468-8-6-4-2-10105-5
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 /          2   \        
-\-2 - 2*cot (x)/*cot(x) 
-------------------------
              4          
       1 + cot (x)
−(−2cot⁡2(x)−2)cot⁡(x)cot⁡4(x)+1- \frac{\left(- 2 \cot^{2}{\left(x \right)} - 2\right) \cot{\left(x \right)}}{\cot^{4}{\left(x \right)} + 1}
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Segunda derivada [src] 
                /                      4    /       2   \\
  /       2   \ |          2      4*cot (x)*\1 + cot (x)/|
2*\1 + cot (x)/*|-1 - 3*cot (x) + -----------------------|
                |                              4         |
                \                       1 + cot (x)      /
----------------------------------------------------------
                              4                           
                       1 + cot (x)
2(cot⁡2(x)+1)(4(cot⁡2(x)+1)cot⁡4(x)cot⁡4(x)+1−3cot⁡2(x)−1)cot⁡4(x)+1\frac{2 \left(\cot^{2}{\left(x \right)} + 1\right) \left(\frac{4 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{4}{\left(x \right)}}{\cot^{4}{\left(x \right)} + 1} - 3 \cot^{2}{\left(x \right)} - 1\right)}{\cot^{4}{\left(x \right)} + 1}
Simplificar
Tercera derivada [src] 
                /                                                         2                          2        \       
                |                     4    /       2   \     /       2   \     2        /       2   \     6   |       
  /       2   \ |         2      6*cot (x)*\1 + cot (x)/   5*\1 + cot (x)/ *cot (x)   8*\1 + cot (x)/ *cot (x)|       
8*\1 + cot (x)/*|2 + 3*cot (x) - ----------------------- - ------------------------ + ------------------------|*cot(x)
                |                             4                         4                               2     |       
                |                      1 + cot (x)               1 + cot (x)               /       4   \      |       
                \                                                                          \1 + cot (x)/      /       
----------------------------------------------------------------------------------------------------------------------
                                                            4                                                         
                                                     1 + cot (x)
8(cot⁡2(x)+1)(−5(cot⁡2(x)+1)2cot⁡2(x)cot⁡4(x)+1+8(cot⁡2(x)+1)2cot⁡6(x)(cot⁡4(x)+1)2−6(cot⁡2(x)+1)cot⁡4(x)cot⁡4(x)+1+3cot⁡2(x)+2)cot⁡(x)cot⁡4(x)+1\frac{8 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- \frac{5 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{2}{\left(x \right)}}{\cot^{4}{\left(x \right)} + 1} + \frac{8 \left(\cot^{2}{\left(x \right)} + 1\right)^{2} \cot^{6}{\left(x \right)}}{\left(\cot^{4}{\left(x \right)} + 1\right)^{2}} - \frac{6 \left(\cot^{2}{\left(x \right)} + 1\right) \cot^{4}{\left(x \right)}}{\cot^{4}{\left(x \right)} + 1} + 3 \cot^{2}{\left(x \right)} + 2\right) \cot{\left(x \right)}}{\cot^{4}{\left(x \right)} + 1}
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Gráfico
Derivada de y=arcctg(ctg^2(x))
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