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y=3ctgx/arcctgx
Derivada de la función/ 3ctgx/ y=3ctg/ y=3ctgx/arcctgx

Derivada de y=3ctgx/arcctgx

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

Ha introducido [src] 
3*cot(x)
--------
acot(x)
3cot⁡(x)acot⁡(x)\frac{3 \cot{\left(x \right)}}{\operatorname{acot}{\left(x \right)}} 
(3*cot(x))/acot(x)
Gráfica
02468-8-6-4-2-1010-200000200000
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Primera derivada [src] 
          2                       
-3 - 3*cot (x)        3*cot(x)    
-------------- + -----------------
   acot(x)       /     2\     2   
                 \1 + x /*acot (x)
−3cot⁡2(x)−3acot⁡(x)+3cot⁡(x)(x2+1)acot⁡2(x)\frac{- 3 \cot^{2}{\left(x \right)} - 3}{\operatorname{acot}{\left(x \right)}} + \frac{3 \cot{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}
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Segunda derivada [src] 
  /                                          /       1   \       \
  |                                2         |x - -------|*cot(x)|
  |/       2   \            1 + cot (x)      \    acot(x)/       |
6*|\1 + cot (x)/*cot(x) - ---------------- - --------------------|
  |                       /     2\                    2          |
  |                       \1 + x /*acot(x)    /     2\           |
  \                                           \1 + x / *acot(x)  /
------------------------------------------------------------------
                             acot(x)
6(−(x−1acot⁡(x))cot⁡(x)(x2+1)2acot⁡(x)+(cot⁡2(x)+1)cot⁡(x)−cot⁡2(x)+1(x2+1)acot⁡(x))acot⁡(x)\frac{6 \left(- \frac{\left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} + \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} - \frac{\cot^{2}{\left(x \right)} + 1}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}
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Tercera derivada [src] 
  /                                  /                             2                    \                                                                \
  |                                  |             3            4*x           6*x       |                                                                |
  |                                  |-1 + ----------------- + ------ - ----------------|*cot(x)                              /       2   \ /       1   \|
  |                                  |     /     2\     2           2   /     2\        |            /       2   \          3*\1 + cot (x)/*|x - -------||
  |  /       2   \ /         2   \   \     \1 + x /*acot (x)   1 + x    \1 + x /*acot(x)/          3*\1 + cot (x)/*cot(x)                   \    acot(x)/|
6*|- \1 + cot (x)/*\1 + 3*cot (x)/ + ----------------------------------------------------------- + ---------------------- + -----------------------------|
  |                                                               2                                   /     2\                            2              |
  |                                                       /     2\                                    \1 + x /*acot(x)            /     2\               |
  \                                                       \1 + x / *acot(x)                                                       \1 + x / *acot(x)      /
----------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                         acot(x)
6(3(x−1acot⁡(x))(cot⁡2(x)+1)(x2+1)2acot⁡(x)−(cot⁡2(x)+1)(3cot⁡2(x)+1)+3(cot⁡2(x)+1)cot⁡(x)(x2+1)acot⁡(x)+(4x2x2+1−6x(x2+1)acot⁡(x)−1+3(x2+1)acot⁡2(x))cot⁡(x)(x2+1)2acot⁡(x))acot⁡(x)\frac{6 \left(\frac{3 \left(x - \frac{1}{\operatorname{acot}{\left(x \right)}}\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}} - \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - \frac{6 x}{\left(x^{2} + 1\right) \operatorname{acot}{\left(x \right)}} - 1 + \frac{3}{\left(x^{2} + 1\right) \operatorname{acot}^{2}{\left(x \right)}}\right) \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2} \operatorname{acot}{\left(x \right)}}\right)}{\operatorname{acot}{\left(x \right)}}
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Gráfico
Derivada de y=3ctgx/arcctgx
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