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y=arccos3x^4/tg^2x
Derivada de la función/ arccos/ tg^2x/ cos3x/ y=arccos3x^4/tg^2x

Derivada de y=arccos3x^4/tg^2x

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    4     
acos (3*x)
----------
    2     
 tan (x)
acos⁡4(3x)tan⁡2(x)\frac{\operatorname{acos}^{4}{\left(3 x \right)}}{\tan^{2}{\left(x \right)}} 
acos(3*x)^4/tan(x)^2
Gráfica
02468-8-6-4-2-1010200000000-100000000
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Trazar el gráfico f'(x)
Primera derivada [src] 
      4      /         2   \              3         
  acos (3*x)*\2 + 2*tan (x)/       12*acos (3*x)    
- -------------------------- - ---------------------
              3                   __________        
           tan (x)               /        2     2   
                               \/  1 - 9*x  *tan (x)
−(2tan⁡2(x)+2)acos⁡4(3x)tan⁡3(x)−12acos⁡3(3x)1−9x2tan⁡2(x)- \frac{\left(2 \tan^{2}{\left(x \right)} + 2\right) \operatorname{acos}^{4}{\left(3 x \right)}}{\tan^{3}{\left(x \right)}} - \frac{12 \operatorname{acos}^{3}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \tan^{2}{\left(x \right)}}
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Segunda derivada [src] 
             /                                       /       /       2   \\                       /       2   \          \
      2      |      54          2      /       2   \ |     3*\1 + tan (x)/|   54*x*acos(3*x)   24*\1 + tan (x)/*acos(3*x)|
2*acos (3*x)*|- --------- + acos (3*x)*\1 + tan (x)/*|-2 + ---------------| - -------------- + --------------------------|
             |          2                            |            2       |             3/2          __________          |
             |  -1 + 9*x                             \         tan (x)    /   /       2\            /        2           |
             \                                                                \1 - 9*x /          \/  1 - 9*x  *tan(x)   /
--------------------------------------------------------------------------------------------------------------------------
                                                            2                                                             
                                                         tan (x)
2(−54xacos⁡(3x)(1−9x2)32+(3(tan⁡2(x)+1)tan⁡2(x)−2)(tan⁡2(x)+1)acos⁡2(3x)−549x2−1+24(tan⁡2(x)+1)acos⁡(3x)1−9x2tan⁡(x))acos⁡2(3x)tan⁡2(x)\frac{2 \left(- \frac{54 x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} - 2\right) \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acos}^{2}{\left(3 x \right)} - \frac{54}{9 x^{2} - 1} + \frac{24 \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acos}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \tan{\left(x \right)}}\right) \operatorname{acos}^{2}{\left(3 x \right)}}{\tan^{2}{\left(x \right)}}
Simplificar
Tercera derivada [src] 
  /     /                      2                              2     2     \                                                                                                                                                                                     \          
  |     |      6           acos (3*x)    27*x*acos(3*x)   27*x *acos (3*x)|                                                                             /       2   \ /    1        x*acos(3*x) \                                         /       /       2   \\|          
  |  27*|------------- + ------------- - -------------- + ----------------|                                                                         162*\1 + tan (x)/*|--------- + -------------|*acos(3*x)          2      /       2   \ |     3*\1 + tan (x)/||          
  |     |          3/2             3/2               2               5/2  |                              /                                     2\                     |        2             3/2|             18*acos (3*x)*\1 + tan (x)/*|-2 + ---------------||          
  |     |/       2\      /       2\       /        2\      /       2\     |                              |      /       2   \     /       2   \ |                     |-1 + 9*x    /       2\   |                                         |            2       ||          
  |     \\1 - 9*x /      \1 - 9*x /       \-1 + 9*x /      \1 - 9*x /     /         3      /       2   \ |    4*\1 + tan (x)/   3*\1 + tan (x)/ |                     \            \1 - 9*x /   /                                         \         tan (x)    /|          
4*|- ---------------------------------------------------------------------- - 2*acos (3*x)*\1 + tan (x)/*|1 - --------------- + ----------------| + ------------------------------------------------------- - --------------------------------------------------|*acos(3*x)
  |                                  tan(x)                                                              |           2                 4        |                              2                                                __________                      |          
  |                                                                                                      \        tan (x)           tan (x)     /                           tan (x)                                            /        2                       |          
  \                                                                                                                                                                                                                          \/  1 - 9*x  *tan(x)               /          
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                   tan(x)
4(162(xacos⁡(3x)(1−9x2)32+19x2−1)(tan⁡2(x)+1)acos⁡(3x)tan⁡2(x)−2(tan⁡2(x)+1)(3(tan⁡2(x)+1)2tan⁡4(x)−4(tan⁡2(x)+1)tan⁡2(x)+1)acos⁡3(3x)−27(27x2acos⁡2(3x)(1−9x2)52−27xacos⁡(3x)(9x2−1)2+acos⁡2(3x)(1−9x2)32+6(1−9x2)32)tan⁡(x)−18(3(tan⁡2(x)+1)tan⁡2(x)−2)(tan⁡2(x)+1)acos⁡2(3x)1−9x2tan⁡(x))acos⁡(3x)tan⁡(x)\frac{4 \left(\frac{162 \left(\frac{x \operatorname{acos}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{1}{9 x^{2} - 1}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acos}{\left(3 x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{4}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 1\right) \operatorname{acos}^{3}{\left(3 x \right)} - \frac{27 \left(\frac{27 x^{2} \operatorname{acos}^{2}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}}} - \frac{27 x \operatorname{acos}{\left(3 x \right)}}{\left(9 x^{2} - 1\right)^{2}} + \frac{\operatorname{acos}^{2}{\left(3 x \right)}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}}}\right)}{\tan{\left(x \right)}} - \frac{18 \left(\frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} - 2\right) \left(\tan^{2}{\left(x \right)} + 1\right) \operatorname{acos}^{2}{\left(3 x \right)}}{\sqrt{1 - 9 x^{2}} \tan{\left(x \right)}}\right) \operatorname{acos}{\left(3 x \right)}}{\tan{\left(x \right)}}
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Gráfico
Derivada de y=arccos3x^4/tg^2x
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