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Derivada de la función/ tan(x)/ cos(3/x)/ 4^tan(x)^(3)*acos(3/x)

Derivada de 4^tan(x)^(3)*acos(3/x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    3           
 tan (x)     /3\
4       *acos|-|
             \x/
4tan⁡3(x)acos⁡(3x)4^{\tan^{3}{\left(x \right)}} \operatorname{acos}{\left(\frac{3}{x} \right)} 
4^(tan(x)^3)*acos(3/x)
Primera derivada [src] 
         3                                                        
      tan (x)          3                                          
   3*4              tan (x)    2    /         2   \     /3\       
---------------- + 4       *tan (x)*\3 + 3*tan (x)/*acos|-|*log(4)
        ________                                        \x/       
 2     /     9                                                    
x *   /  1 - --                                                   
     /        2                                                   
   \/        x
4tan⁡3(x)(3tan⁡2(x)+3)log⁡(4)tan⁡2(x)acos⁡(3x)+3⋅4tan⁡3(x)x21−9x24^{\tan^{3}{\left(x \right)}} \left(3 \tan^{2}{\left(x \right)} + 3\right) \log{\left(4 \right)} \tan^{2}{\left(x \right)} \operatorname{acos}{\left(\frac{3}{x} \right)} + \frac{3 \cdot 4^{\tan^{3}{\left(x \right)}}}{x^{2} \sqrt{1 - \frac{9}{x^{2}}}}
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Segunda derivada [src] 
           /           9                                                                                                                              \
           |  2 + -----------                                                                                                                         |
           |       2 /    9 \                                                                                                                         |
           |      x *|1 - --|                                                                                                                         |
      3    |         |     2|                                                                                                2    /       2   \       |
   tan (x) |         \    x /    /       2   \ /         2           3    /       2   \       \     /3\                 6*tan (x)*\1 + tan (x)/*log(4)|
3*4       *|- ---------------- + \1 + tan (x)/*\2 + 4*tan (x) + 3*tan (x)*\1 + tan (x)/*log(4)/*acos|-|*log(4)*tan(x) + ------------------------------|
           |          ________                                                                      \x/                                ________       |
           |   3     /     9                                                                                                    2     /     9         |
           |  x *   /  1 - --                                                                                                  x *   /  1 - --        |
           |       /        2                                                                                                       /        2        |
           \     \/        x                                                                                                      \/        x         /
3⋅4tan⁡3(x)((tan⁡2(x)+1)(3(tan⁡2(x)+1)log⁡(4)tan⁡3(x)+4tan⁡2(x)+2)log⁡(4)tan⁡(x)acos⁡(3x)+6(tan⁡2(x)+1)log⁡(4)tan⁡2(x)x21−9x2−2+9x2(1−9x2)x31−9x2)3 \cdot 4^{\tan^{3}{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 \right)} \tan^{3}{\left(x \right)} + 4 \tan^{2}{\left(x \right)} + 2\right) \log{\left(4 \right)} \tan{\left(x \right)} \operatorname{acos}{\left(\frac{3}{x} \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 \right)} \tan^{2}{\left(x \right)}}{x^{2} \sqrt{1 - \frac{9}{x^{2}}}} - \frac{2 + \frac{9}{x^{2} \left(1 - \frac{9}{x^{2}}\right)}}{x^{3} \sqrt{1 - \frac{9}{x^{2}}}}\right)
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Tercera derivada [src] 
           /  /         21            81     \                                                                                                                                                                                                                                                                                                                                     \
           |3*|2 + ----------- + ------------|                                                                                                                                                                                                         2    /       2   \ /         9     \                                                                                        |
           |  |     2 /    9 \              2|                                                                                                                                                                                                    9*tan (x)*\1 + tan (x)/*|2 + -----------|*log(4)                                                                                 |
           |  |    x *|1 - --|    4 /    9 \ |                                                                                                                                                                                                                            |     2 /    9 \|                                                                                        |
           |  |       |     2|   x *|1 - --| |                                                                                                                                                                                                                            |    x *|1 - --||                                                                                        |
      3    |  |       \    x /      |     2| |                 /               2                                                         2                                   2                                                 \                                          |       |     2||            /       2   \ /         2           3    /       2   \       \              |
   tan (x) |  \                     \    x / /   /       2   \ |  /       2   \         4            2    /       2   \     /       2   \     2       6         /       2   \     3                   5    /       2   \       |     /3\                                  \       \    x //          9*\1 + tan (x)/*\2 + 4*tan (x) + 3*tan (x)*\1 + tan (x)/*log(4)/*log(4)*tan(x)|
3*4       *|---------------------------------- + \1 + tan (x)/*\2*\1 + tan (x)/  + 4*tan (x) + 14*tan (x)*\1 + tan (x)/ + 9*\1 + tan (x)/ *log (4)*tan (x) + 18*\1 + tan (x)/ *tan (x)*log(4) + 18*tan (x)*\1 + tan (x)/*log(4)/*acos|-|*log(4) - ------------------------------------------------ + ------------------------------------------------------------------------------|
           |                 ________                                                                                                                                                                                                \x/                                  ________                                                          ________                               |
           |          4     /     9                                                                                                                                                                                                                                3     /     9                                                     2     /     9                                 |
           |         x *   /  1 - --                                                                                                                                                                                                                              x *   /  1 - --                                                   x *   /  1 - --                                |
           |              /        2                                                                                                                                                                                                                                   /        2                                                        /        2                                |
           \            \/        x                                                                                                                                                                                                                                  \/        x                                                       \/        x                                 /
3⋅4tan⁡3(x)((tan⁡2(x)+1)(9(tan⁡2(x)+1)2log⁡(4)2tan⁡6(x)+18(tan⁡2(x)+1)2log⁡(4)tan⁡3(x)+2(tan⁡2(x)+1)2+18(tan⁡2(x)+1)log⁡(4)tan⁡5(x)+14(tan⁡2(x)+1)tan⁡2(x)+4tan⁡4(x))log⁡(4)acos⁡(3x)+9(tan⁡2(x)+1)(3(tan⁡2(x)+1)log⁡(4)tan⁡3(x)+4tan⁡2(x)+2)log⁡(4)tan⁡(x)x21−9x2−9(2+9x2(1−9x2))(tan⁡2(x)+1)log⁡(4)tan⁡2(x)x31−9x2+3(2+21x2(1−9x2)+81x4(1−9x2)2)x41−9x2)3 \cdot 4^{\tan^{3}{\left(x \right)}} \left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(9 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(4 \right)}^{2} \tan^{6}{\left(x \right)} + 18 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(4 \right)} \tan^{3}{\left(x \right)} + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 18 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 \right)} \tan^{5}{\left(x \right)} + 14 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + 4 \tan^{4}{\left(x \right)}\right) \log{\left(4 \right)} \operatorname{acos}{\left(\frac{3}{x} \right)} + \frac{9 \left(\tan^{2}{\left(x \right)} + 1\right) \left(3 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 \right)} \tan^{3}{\left(x \right)} + 4 \tan^{2}{\left(x \right)} + 2\right) \log{\left(4 \right)} \tan{\left(x \right)}}{x^{2} \sqrt{1 - \frac{9}{x^{2}}}} - \frac{9 \left(2 + \frac{9}{x^{2} \left(1 - \frac{9}{x^{2}}\right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(4 \right)} \tan^{2}{\left(x \right)}}{x^{3} \sqrt{1 - \frac{9}{x^{2}}}} + \frac{3 \left(2 + \frac{21}{x^{2} \left(1 - \frac{9}{x^{2}}\right)} + \frac{81}{x^{4} \left(1 - \frac{9}{x^{2}}\right)^{2}}\right)}{x^{4} \sqrt{1 - \frac{9}{x^{2}}}}\right)
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