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x*exp(-x)log3(7x^3-e)/(3^(2x)-tg^2x)
Derivada de la función/ x*exp(-x)log3(7x^3-e)/(3^(2x)-tg^2x)

Derivada de x*exp(-x)log3(7x^3-e)/(3^(2x)-tg^2x)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
         /   3    \
   -x log\7*x  - E/
x*e  *-------------
          log(3)   
-------------------
    2*x      2     
   3    - tan (x)
xe−xlog⁡(7x3−e)log⁡(3)32x−tan⁡2(x)\frac{x e^{- x} \frac{\log{\left(7 x^{3} - e \right)}}{\log{\left(3 \right)}}}{3^{2 x} - \tan^{2}{\left(x \right)}} 
((x*exp(-x))*(log(7*x^3 - E)/log(3)))/(3^(2*x) - tan(x)^2)
Gráfica
02468-8-6-4-2-1010-200100
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Primera derivada [src] 
/     -x    -x\    /   3    \           3  -x                                                                   
\- x*e   + e  /*log\7*x  - E/       21*x *e                                                                     
----------------------------- + -----------------                                                               
            log(3)              /   3    \            //         2   \             2*x       \  -x    /   3    \
                                \7*x  - E/*log(3)   x*\\2 + 2*tan (x)/*tan(x) - 2*3   *log(3)/*e  *log\7*x  - E/
------------------------------------------------- + ------------------------------------------------------------
                   2*x      2                                                         2                         
                  3    - tan (x)                                      / 2*x      2   \                          
                                                                      \3    - tan (x)/ *log(3)
x(−2⋅32xlog⁡(3)+(2tan⁡2(x)+2)tan⁡(x))e−xlog⁡(7x3−e)(32x−tan⁡2(x))2log⁡(3)+21x3e−x(7x3−e)log⁡(3)+(−xe−x+e−x)log⁡(7x3−e)log⁡(3)32x−tan⁡2(x)\frac{x \left(- 2 \cdot 3^{2 x} \log{\left(3 \right)} + \left(2 \tan^{2}{\left(x \right)} + 2\right) \tan{\left(x \right)}\right) e^{- x} \log{\left(7 x^{3} - e \right)}}{\left(3^{2 x} - \tan^{2}{\left(x \right)}\right)^{2} \log{\left(3 \right)}} + \frac{\frac{21 x^{3} e^{- x}}{\left(7 x^{3} - e\right) \log{\left(3 \right)}} + \frac{\left(- x e^{- x} + e^{- x}\right) \log{\left(7 x^{3} - e \right)}}{\log{\left(3 \right)}}}{3^{2 x} - \tan^{2}{\left(x \right)}}
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Segunda derivada [src] 
/                                                                                                                                                         /                                                                                                  2\               \    
|                                                 /           3  \                                          /                                  3  \       |             2                                                / 2*x          /       2   \       \ |               |    
|                                               2 |       21*x   |     / 2*x          /       2   \       \ |              /        3\     21*x   |       |/       2   \       2*x    2           2    /       2   \   4*\3   *log(3) - \1 + tan (x)/*tan(x)/ |    /        3\|    
|                                           21*x *|-2 + ---------|   4*\3   *log(3) - \1 + tan (x)/*tan(x)/*|- (-1 + x)*log\-E + 7*x / + ---------|   2*x*|\1 + tan (x)/  - 2*3   *log (3) + 2*tan (x)*\1 + tan (x)/ + ---------------------------------------|*log\-E + 7*x /|    
|                              2                  |             3|                                          |                                    3|       |                                                                          2*x      2               |               |    
|            /        3\   42*x *(-1 + x)         \     -E + 7*x /                                          \                            -E + 7*x /       \                                                                         3    - tan (x)            /               |  -x
|(-2 + x)*log\-E + 7*x / - -------------- - ---------------------- - ------------------------------------------------------------------------------ + ------------------------------------------------------------------------------------------------------------------------|*e  
|                                    3                    3                                           2*x      2                                                                                            2*x      2                                                        |    
\                            -E + 7*x             -E + 7*x                                           3    - tan (x)                                                                                        3    - tan (x)                                                     /    
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                              / 2*x      2   \                                                                                                                                     
                                                                                                                              \3    - tan (x)/*log(3)
(−42x2(x−1)7x3−e−21x2(21x37x3−e−2)7x3−e+2x(−2⋅32xlog⁡(3)2+(tan⁡2(x)+1)2+2(tan⁡2(x)+1)tan⁡2(x)+4(32xlog⁡(3)−(tan⁡2(x)+1)tan⁡(x))232x−tan⁡2(x))log⁡(7x3−e)32x−tan⁡2(x)+(x−2)log⁡(7x3−e)−4(32xlog⁡(3)−(tan⁡2(x)+1)tan⁡(x))(21x37x3−e−(x−1)log⁡(7x3−e))32x−tan⁡2(x))e−x(32x−tan⁡2(x))log⁡(3)\frac{\left(- \frac{42 x^{2} \left(x - 1\right)}{7 x^{3} - e} - \frac{21 x^{2} \left(\frac{21 x^{3}}{7 x^{3} - e} - 2\right)}{7 x^{3} - e} + \frac{2 x \left(- 2 \cdot 3^{2 x} \log{\left(3 \right)}^{2} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{4 \left(3^{2 x} \log{\left(3 \right)} - \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{2}}{3^{2 x} - \tan^{2}{\left(x \right)}}\right) \log{\left(7 x^{3} - e \right)}}{3^{2 x} - \tan^{2}{\left(x \right)}} + \left(x - 2\right) \log{\left(7 x^{3} - e \right)} - \frac{4 \left(3^{2 x} \log{\left(3 \right)} - \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(\frac{21 x^{3}}{7 x^{3} - e} - \left(x - 1\right) \log{\left(7 x^{3} - e \right)}\right)}{3^{2 x} - \tan^{2}{\left(x \right)}}\right) e^{- x}}{\left(3^{2 x} - \tan^{2}{\left(x \right)}\right) \log{\left(3 \right)}}
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Tercera derivada [src] 
/                                                                   /                                  /           3  \                 \                                                                                                                                                                                                                                                                                                                                                                                                                                                                               \    
|                                                                   |                                2 |       21*x   |                 |                                                                                                                                                                                                                /                                                                                                       3                                          /             2                                           \\                                                |    
|                                                                   |                            21*x *|-2 + ---------|                 |                                             /                                                                                                  2\        /          3             6   \                        |                                                      2            / 2*x          /       2   \       \      / 2*x          /       2   \       \ |/       2   \       2*x    2           2    /       2   \||                                                |    
|                                                                   |                                  |             3|       2         |     /                                  3  \ |             2                                                / 2*x          /       2   \       \ |        |      63*x         441*x    |                        | 2*x    3         3    /       2   \     /       2   \           6*\3   *log(3) - \1 + tan (x)/*tan(x)/    3*\3   *log(3) - \1 + tan (x)/*tan(x)/*\\1 + tan (x)/  - 2*3   *log (3) + 2*tan (x)*\1 + tan (x)//|    /        3\                 /           3  \|    
|                              / 2*x          /       2   \       \ |              /        3\         \     -E + 7*x /   42*x *(-1 + x)|     |              /        3\     21*x   | |/       2   \       2*x    2           2    /       2   \   4*\3   *log(3) - \1 + tan (x)/*tan(x)/ |   42*x*|1 - --------- + ------------|                    8*x*|3   *log (3) - tan (x)*\1 + tan (x)/ - 2*\1 + tan (x)/ *tan(x) + --------------------------------------- + --------------------------------------------------------------------------------------------------|*log\-E + 7*x /                 |       21*x   ||    
|                            6*\3   *log(3) - \1 + tan (x)/*tan(x)/*|- (-2 + x)*log\-E + 7*x / + ---------------------- + --------------|   6*|- (-1 + x)*log\-E + 7*x / + ---------|*|\1 + tan (x)/  - 2*3   *log (3) + 2*tan (x)*\1 + tan (x)/ + ---------------------------------------|        |            3              2|                        |                                                                                            2                                                         2*x      2                                             |                  63*x*(-1 + x)*|-2 + ---------||    
|                                                                   |                                          3                    3   |     |                                    3| |                                                                          2*x      2               |        |    -E + 7*x    /        3\ |       2                |                                                                            / 2*x      2   \                                                         3    - tan (x)                                          |                                |             3||    
|              /        3\                                          \                                  -E + 7*x             -E + 7*x    /     \                            -E + 7*x / \                                                                         3    - tan (x)            /        \                \-E + 7*x / /   63*x *(-2 + x)       \                                                                            \3    - tan (x)/                                                                                                                 /                                \     -E + 7*x /|  -x
|- (-3 + x)*log\-E + 7*x / + ------------------------------------------------------------------------------------------------------------ + ----------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------- + -------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------|*e  
|                                                                            2*x      2                                                                                                                       2*x      2                                                                                           3                          3                                                                                                                 2*x      2                                                                                                                                  3           |    
\                                                                           3    - tan (x)                                                                                                                   3    - tan (x)                                                                                -E + 7*x                   -E + 7*x                                                                                                                 3    - tan (x)                                                                                                                       -E + 7*x            /    
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                   / 2*x      2   \                                                                                                                                                                                                                                                                                                          
                                                                                                                                                                                                                                                                                                   \3    - tan (x)/*log(3)
(63x2(x−2)7x3−e+63x(x−1)(21x37x3−e−2)7x3−e+42x(441x6(7x3−e)2−63x37x3−e+1)7x3−e−8x(32xlog⁡(3)3−2(tan⁡2(x)+1)2tan⁡(x)−(tan⁡2(x)+1)tan⁡3(x)+3(32xlog⁡(3)−(tan⁡2(x)+1)tan⁡(x))(−2⋅32xlog⁡(3)2+(tan⁡2(x)+1)2+2(tan⁡2(x)+1)tan⁡2(x))32x−tan⁡2(x)+6(32xlog⁡(3)−(tan⁡2(x)+1)tan⁡(x))3(32x−tan⁡2(x))2)log⁡(7x3−e)32x−tan⁡2(x)−(x−3)log⁡(7x3−e)+6(32xlog⁡(3)−(tan⁡2(x)+1)tan⁡(x))(42x2(x−1)7x3−e+21x2(21x37x3−e−2)7x3−e−(x−2)log⁡(7x3−e))32x−tan⁡2(x)+6(21x37x3−e−(x−1)log⁡(7x3−e))(−2⋅32xlog⁡(3)2+(tan⁡2(x)+1)2+2(tan⁡2(x)+1)tan⁡2(x)+4(32xlog⁡(3)−(tan⁡2(x)+1)tan⁡(x))232x−tan⁡2(x))32x−tan⁡2(x))e−x(32x−tan⁡2(x))log⁡(3)\frac{\left(\frac{63 x^{2} \left(x - 2\right)}{7 x^{3} - e} + \frac{63 x \left(x - 1\right) \left(\frac{21 x^{3}}{7 x^{3} - e} - 2\right)}{7 x^{3} - e} + \frac{42 x \left(\frac{441 x^{6}}{\left(7 x^{3} - e\right)^{2}} - \frac{63 x^{3}}{7 x^{3} - e} + 1\right)}{7 x^{3} - e} - \frac{8 x \left(3^{2 x} \log{\left(3 \right)}^{3} - 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \tan{\left(x \right)} - \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{3}{\left(x \right)} + \frac{3 \left(3^{2 x} \log{\left(3 \right)} - \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(- 2 \cdot 3^{2 x} \log{\left(3 \right)}^{2} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)}\right)}{3^{2 x} - \tan^{2}{\left(x \right)}} + \frac{6 \left(3^{2 x} \log{\left(3 \right)} - \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{3}}{\left(3^{2 x} - \tan^{2}{\left(x \right)}\right)^{2}}\right) \log{\left(7 x^{3} - e \right)}}{3^{2 x} - \tan^{2}{\left(x \right)}} - \left(x - 3\right) \log{\left(7 x^{3} - e \right)} + \frac{6 \left(3^{2 x} \log{\left(3 \right)} - \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right) \left(\frac{42 x^{2} \left(x - 1\right)}{7 x^{3} - e} + \frac{21 x^{2} \left(\frac{21 x^{3}}{7 x^{3} - e} - 2\right)}{7 x^{3} - e} - \left(x - 2\right) \log{\left(7 x^{3} - e \right)}\right)}{3^{2 x} - \tan^{2}{\left(x \right)}} + \frac{6 \left(\frac{21 x^{3}}{7 x^{3} - e} - \left(x - 1\right) \log{\left(7 x^{3} - e \right)}\right) \left(- 2 \cdot 3^{2 x} \log{\left(3 \right)}^{2} + \left(\tan^{2}{\left(x \right)} + 1\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \tan^{2}{\left(x \right)} + \frac{4 \left(3^{2 x} \log{\left(3 \right)} - \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}\right)^{2}}{3^{2 x} - \tan^{2}{\left(x \right)}}\right)}{3^{2 x} - \tan^{2}{\left(x \right)}}\right) e^{- x}}{\left(3^{2 x} - \tan^{2}{\left(x \right)}\right) \log{\left(3 \right)}}
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Gráfico
Derivada de x*exp(-x)log3(7x^3-e)/(3^(2x)-tg^2x)
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