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y=(tgx)arctg
Derivada de la función/ arctg/ (tgx)/ y=(tgx)arctg

Derivada de y=(tgx)arctg

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

Gráfico:

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Solución

Ha introducido [src] 
tan(x)*atan(x)
tan⁡(x)atan⁡(x)\tan{\left(x \right)} \operatorname{atan}{\left(x \right)} 
tan(x)*atan(x)
Gráfica
02468-8-6-4-2-1010-25002500
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Trazar el gráfico f'(x)
Primera derivada [src] 
tan(x)   /       2   \        
------ + \1 + tan (x)/*atan(x)
     2                        
1 + x
(tan⁡2(x)+1)atan⁡(x)+tan⁡(x)x2+1\left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{atan}{\left(x \right)} + \frac{\tan{\left(x \right)}}{x^{2} + 1}
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Segunda derivada [src] 
  /       2                                              \
  |1 + tan (x)   /       2   \                   x*tan(x)|
2*|----------- + \1 + tan (x)/*atan(x)*tan(x) - ---------|
  |        2                                            2|
  |   1 + x                                     /     2\ |
  \                                             \1 + x / /
2(−xtan⁡(x)(x2+1)2+(tan⁡2(x)+1)tan⁡(x)atan⁡(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{atan}{\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   \       |
  |\     1 + x /          /       2   \ /         2   \           3*x*\1 + tan (x)/   3*\1 + tan (x)/*tan(x)|
2*|-------------------- + \1 + tan (x)/*\1 + 3*tan (x)/*atan(x) - ----------------- + ----------------------|
  |             2                                                             2                    2        |
  |     /     2\                                                      /     2\                1 + x         |
  \     \1 + x /                                                      \1 + x /                              /
2(−3x(tan⁡2(x)+1)(x2+1)2+(tan⁡2(x)+1)(3tan⁡2(x)+1)atan⁡(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{atan}{\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 y=(tgx)arctg
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