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tg(x)*arcctg(x)
Derivada de la función/ tg(x)/ tg(x)*arcctg(x)

Derivada de tg(x)*arcctg(x)

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

Ha introducido [src] 
tan(x)*acot(x)
tan⁡(x)acot⁡(x)\tan{\left(x \right)} \operatorname{acot}{\left(x \right)} 
tan(x)*acot(x)
Gráfica
02468-8-6-4-2-1010-500500
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Trazar el gráfico f'(x)
Primera derivada [src] 
/       2   \           tan(x)
\1 + tan (x)/*acot(x) - ------
                             2
                        1 + x
(tan⁡2(x)+1)acot⁡(x)−tan⁡(x)x2+1\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)} - \frac{\tan{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
  /         2                                              \
  |  1 + tan (x)    x*tan(x)   /       2   \               |
2*|- ----------- + --------- + \1 + tan (x)/*acot(x)*tan(x)|
  |          2             2                               |
  |     1 + x      /     2\                                |
  \                \1 + x /                                /
2(xtan⁡(x)(x2+1)2+(tan⁡2(x)+1)tan⁡(x)acot⁡(x)−tan⁡2(x)+1x2+1)2 \left(\frac{x \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} \operatorname{acot}{\left(x \right)} - \frac{\tan^{2}{\left(x \right)} + 1}{x^{2} + 1}\right)
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Tercera derivada [src] 
  /                                        /         2 \                                                    \
  |                                        |      4*x  |                                                    |
  |                                        |-1 + ------|*tan(x)                                             |
  |                                        |          2|            /       2   \              /       2   \|
  |/       2   \ /         2   \           \     1 + x /          3*\1 + tan (x)/*tan(x)   3*x*\1 + tan (x)/|
2*|\1 + tan (x)/*\1 + 3*tan (x)/*acot(x) - -------------------- - ---------------------- + -----------------|
  |                                                     2                      2                       2    |
  |                                             /     2\                  1 + x                /     2\     |
  \                                             \1 + x /                                       \1 + x /     /
2(3x(tan⁡2(x)+1)(x2+1)2+(tan⁡2(x)+1)(3tan⁡2(x)+1)acot⁡(x)−3(tan⁡2(x)+1)tan⁡(x)x2+1−(4x2x2+1−1)tan⁡(x)(x2+1)2)2 \left(\frac{3 x \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right) \operatorname{acot}{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2} + 1} - \frac{\left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}\right)
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Gráfico
Derivada de tg(x)*arcctg(x)
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