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

Derivada de y=ctgx*arcctgx

Función f() - derivada -er orden en el punto
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Ha introducido [src] 
cot(x)*acot(x)
cot⁡(x)acot⁡(x)\cot{\left(x \right)} \operatorname{acot}{\left(x \right)} 
cot(x)*acot(x)
Gráfica
02468-8-6-4-2-1010-50005000
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Primera derivada [src] 
/        2   \           cot(x)
\-1 - cot (x)/*acot(x) - ------
                              2
                         1 + x
(−cot⁡2(x)−1)acot⁡(x)−cot⁡(x)x2+1\left(- \cot^{2}{\left(x \right)} - 1\right) \operatorname{acot}{\left(x \right)} - \frac{\cot{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
  /       2                                              \
  |1 + cot (x)    x*cot(x)   /       2   \               |
2*|----------- + --------- + \1 + cot (x)/*acot(x)*cot(x)|
  |        2             2                               |
  |   1 + x      /     2\                                |
  \              \1 + x /                                /
2(xcot⁡(x)(x2+1)2+(cot⁡2(x)+1)cot⁡(x)acot⁡(x)+cot⁡2(x)+1x2+1)2 \left(\frac{x \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)} \operatorname{acot}{\left(x \right)} + \frac{\cot^{2}{\left(x \right)} + 1}{x^{2} + 1}\right)
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Tercera derivada [src] 
   //         2 \                                                                                            \
   ||      4*x  |                                                                                            |
   ||-1 + ------|*cot(x)                                                                                     |
   ||          2|                                                      /       2   \     /       2   \       |
   |\     1 + x /          /       2   \ /         2   \           3*x*\1 + cot (x)/   3*\1 + cot (x)/*cot(x)|
-2*|-------------------- + \1 + cot (x)/*\1 + 3*cot (x)/*acot(x) + ----------------- + ----------------------|
   |             2                                                             2                    2        |
   |     /     2\                                                      /     2\                1 + x         |
   \     \1 + x /                                                      \1 + x /                              /
−2(3x(cot⁡2(x)+1)(x2+1)2+(cot⁡2(x)+1)(3cot⁡2(x)+1)acot⁡(x)+3(cot⁡2(x)+1)cot⁡(x)x2+1+(4x2x2+1−1)cot⁡(x)(x2+1)2)- 2 \left(\frac{3 x \left(\cot^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} + \left(\cot^{2}{\left(x \right)} + 1\right) \left(3 \cot^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)} + \frac{3 \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{x^{2} + 1} + \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \cot{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de y=ctgx*arcctgx
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