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y=(tgx/3)/arctg4x
Derivada de la función/ ctg4x/ arctg/ y=(tgx/3)/arctg4x

Derivada de y=(tgx/3)/arctg4x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 /tan(x)\
 |------|
 \  3   /
---------
atan(4*x)
13tan⁡(x)atan⁡(4x)\frac{\frac{1}{3} \tan{\left(x \right)}}{\operatorname{atan}{\left(4 x \right)}} 
(tan(x)/3)/atan(4*x)
Gráfica
02468-8-6-4-2-1010-500500
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Trazar el gráfico f'(x)
Primera derivada [src] 
       2                              
1   tan (x)                           
- + -------                           
3      3              4*tan(x)        
----------- - ------------------------
 atan(4*x)      /        2\     2     
              3*\1 + 16*x /*atan (4*x)
tan⁡2(x)3+13atan⁡(4x)−4tan⁡(x)3(16x2+1)atan⁡2(4x)\frac{\frac{\tan^{2}{\left(x \right)}}{3} + \frac{1}{3}}{\operatorname{atan}{\left(4 x \right)}} - \frac{4 \tan{\left(x \right)}}{3 \left(16 x^{2} + 1\right) \operatorname{atan}^{2}{\left(4 x \right)}}
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Segunda derivada [src] 
  /                                                  /    1          \       \
  |                            /       2   \      16*|--------- + 4*x|*tan(x)|
  |/       2   \             4*\1 + tan (x)/         \atan(4*x)      /       |
2*|\1 + tan (x)/*tan(x) - --------------------- + ---------------------------|
  |                       /        2\                           2            |
  |                       \1 + 16*x /*atan(4*x)      /        2\             |
  \                                                  \1 + 16*x / *atan(4*x)  /
------------------------------------------------------------------------------
                                 3*atan(4*x)
2(16(4x+1atan⁡(4x))tan⁡(x)(16x2+1)2atan⁡(4x)+(tan⁡2(x)+1)tan⁡(x)−4(tan⁡2(x)+1)(16x2+1)atan⁡(4x))3atan⁡(4x)\frac{2 \left(\frac{16 \left(4 x + \frac{1}{\operatorname{atan}{\left(4 x \right)}}\right) \tan{\left(x \right)}}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}}\right)}{3 \operatorname{atan}{\left(4 x \right)}}
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Tercera derivada [src] 
  /                                                                                                 /                                    2                          \       \
  |                                                                                                 |               3                64*x               24*x        |       |
  |                                                            /       2   \ /    1          \   64*|-1 + ---------------------- + --------- + ---------------------|*tan(x)|
  |/       2   \ /         2   \     /       2   \          16*\1 + tan (x)/*|--------- + 4*x|      |     /        2\     2                2   /        2\          |       |
  |\1 + tan (x)/*\1 + 3*tan (x)/   4*\1 + tan (x)/*tan(x)                    \atan(4*x)      /      \     \1 + 16*x /*atan (4*x)   1 + 16*x    \1 + 16*x /*atan(4*x)/       |
2*|----------------------------- - ---------------------- + ---------------------------------- - ---------------------------------------------------------------------------|
  |              3                 /        2\                               2                                                          2                                   |
  |                                \1 + 16*x /*atan(4*x)          /        2\                                                /        2\                                    |
  \                                                               \1 + 16*x / *atan(4*x)                                   3*\1 + 16*x / *atan(4*x)                         /
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                  atan(4*x)
2(16(4x+1atan⁡(4x))(tan⁡2(x)+1)(16x2+1)2atan⁡(4x)+(tan⁡2(x)+1)(3tan⁡2(x)+1)3−4(tan⁡2(x)+1)tan⁡(x)(16x2+1)atan⁡(4x)−64(64x216x2+1+24x(16x2+1)atan⁡(4x)−1+3(16x2+1)atan⁡2(4x))tan⁡(x)3(16x2+1)2atan⁡(4x))atan⁡(4x)\frac{2 \left(\frac{16 \left(4 x + \frac{1}{\operatorname{atan}{\left(4 x \right)}}\right) \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}} + \frac{\left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \tan^{2}{\left(x \right)} + 1\right)}{3} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - \frac{64 \left(\frac{64 x^{2}}{16 x^{2} + 1} + \frac{24 x}{\left(16 x^{2} + 1\right) \operatorname{atan}{\left(4 x \right)}} - 1 + \frac{3}{\left(16 x^{2} + 1\right) \operatorname{atan}^{2}{\left(4 x \right)}}\right) \tan{\left(x \right)}}{3 \left(16 x^{2} + 1\right)^{2} \operatorname{atan}{\left(4 x \right)}}\right)}{\operatorname{atan}{\left(4 x \right)}}
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Gráfico
Derivada de y=(tgx/3)/arctg4x
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