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(x*exp(-x)+(2*sinx/(cos(x))^2)+1-exp(-x))/(x+2/cos(x)-x*exp(-x))
Derivada de la función/ (x*exp(-x)+(2*sinx/(cos(x))^2)+1-exp(-x))/(x+2/cos(x)-x*exp(-x))

Derivada de (x*exp(-x)+(2*sinx/(cos(x))^2)+1-exp(-x))/(x+2/cos(x)-x*exp(-x))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   -x   2*sin(x)        -x
x*e   + -------- + 1 - e  
           2              
        cos (x)           
--------------------------
          2         -x    
    x + ------ - x*e      
        cos(x)
((xe−x+2sin⁡(x)cos⁡2(x))+1)−e−x−xe−x+(x+2cos⁡(x))\frac{\left(\left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) + 1\right) - e^{- x}}{- x e^{- x} + \left(x + \frac{2}{\cos{\left(x \right)}}\right)} 
(x*exp(-x) + (2*sin(x))/cos(x)^2 + 1 - exp(-x))/(x + 2/cos(x) - x*exp(-x))
Gráfica
02468-8-6-4-2-1010-10001000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                2                                                                
   -x      -x   2*cos(x)   4*sin (x)   /   -x   2*sin(x)        -x\ /        -x   2*sin(x)    -x\
2*e   - x*e   + -------- + ---------   |x*e   + -------- + 1 - e  |*|-1 - x*e   - -------- + e  |
                   2           3       |           2              | |                2          |
                cos (x)     cos (x)    \        cos (x)           / \             cos (x)       /
------------------------------------ + ----------------------------------------------------------
               2         -x                                                  2                   
         x + ------ - x*e                                /      2         -x\                    
             cos(x)                                      |x + ------ - x*e  |                    
                                                         \    cos(x)        /
−xe−x+4sin⁡2(x)cos⁡3(x)+2cos⁡(x)cos⁡2(x)+2e−x−xe−x+(x+2cos⁡(x))+(((xe−x+2sin⁡(x)cos⁡2(x))+1)−e−x)(−xe−x−2sin⁡(x)cos⁡2(x)−1+e−x)(−xe−x+(x+2cos⁡(x)))2\frac{- x e^{- x} + \frac{4 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2 \cos{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 2 e^{- x}}{- x e^{- x} + \left(x + \frac{2}{\cos{\left(x \right)}}\right)} + \frac{\left(\left(\left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}}\right) + 1\right) - e^{- x}\right) \left(- x e^{- x} - \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 1 + e^{- x}\right)}{\left(- x e^{- x} + \left(x + \frac{2}{\cos{\left(x \right)}}\right)\right)^{2}}
Simplificar
Segunda derivada [src] 
                                                                        /                                                       2            \                                                                      
                                                                        |                           /     -x      -x   2*sin(x)\             |                                                                      
                                                                        |                         2*|1 - e   + x*e   + --------|             |                                                                      
                                                                        |                           |                     2    |         2   |                                                                      
                                           /     -x      -x   2*sin(x)\ |  2         -x      -x     \                  cos (x) /    4*sin (x)|                                  /                              2   \
                                           |1 - e   + x*e   + --------|*|------ + 2*e   - x*e   - ------------------------------- + ---------|     /     -x      -x   2*sin(x)\ |  2         -x      -x   4*sin (x)|
                                           |                     2    | |cos(x)                                2         -x             3    |   2*|1 - e   + x*e   + --------|*|------ + 2*e   - x*e   + ---------|
                                    3      \                  cos (x) / |                                x + ------ - x*e            cos (x) |     |                     2    | |cos(x)                       3    |
     -x      -x   10*sin(x)   12*sin (x)                                \                                    cos(x)                          /     \                  cos (x) / \                          cos (x) /
- 3*e   + x*e   + --------- + ---------- - --------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------
                      2           4                                                       2         -x                                                                          2         -x                        
                   cos (x)     cos (x)                                              x + ------ - x*e                                                                      x + ------ - x*e                          
                                                                                        cos(x)                                                                                cos(x)                                
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                       2         -x                                                                                                 
                                                                                                 x + ------ - x*e                                                                                                   
                                                                                                     cos(x)
xe−x+12sin⁡3(x)cos⁡4(x)+10sin⁡(x)cos⁡2(x)−3e−x−2(−xe−x+4sin⁡2(x)cos⁡3(x)+2cos⁡(x)+2e−x)(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)x−xe−x+2cos⁡(x)−(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)(−xe−x+4sin⁡2(x)cos⁡3(x)+2cos⁡(x)+2e−x−2(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)2x−xe−x+2cos⁡(x))x−xe−x+2cos⁡(x)x−xe−x+2cos⁡(x)\frac{x e^{- x} + \frac{12 \sin^{3}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{10 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 3 e^{- x} - \frac{2 \left(- x e^{- x} + \frac{4 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2}{\cos{\left(x \right)}} + 2 e^{- x}\right) \left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right)}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}} - \frac{\left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right) \left(- x e^{- x} + \frac{4 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2}{\cos{\left(x \right)}} + 2 e^{- x} - \frac{2 \left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right)^{2}}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}}\right)}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}}}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}}
Simplificar
Tercera derivada [src] 
                                                                                /                                                3                                                           /                              2   \\                                                                                                                                                                                            
                                                                                |                    /     -x      -x   2*sin(x)\                               /     -x      -x   2*sin(x)\ |  2         -x      -x   4*sin (x)||                                                                                                                      /                                                       2            \
                                                                                |                  6*|1 - e   + x*e   + --------|                             6*|1 - e   + x*e   + --------|*|------ + 2*e   - x*e   + ---------||                                                                                                                      |                           /     -x      -x   2*sin(x)\             |
                                                                                |                    |                     2    |                      3        |                     2    | |cos(x)                       3    ||                                                                                                                      |                         2*|1 - e   + x*e   + --------|             |
                                                   /     -x      -x   2*sin(x)\ |     -x      -x     \                  cos (x) /    10*sin(x)   12*sin (x)     \                  cos (x) / \                          cos (x) /|                                                                                 /                              2   \ |                           |                     2    |         2   |
                                                   |1 - e   + x*e   + --------|*|- 3*e   + x*e   + ------------------------------- + --------- + ---------- - -------------------------------------------------------------------|                                  /                                    3   \     |  2         -x      -x   4*sin (x)| |  2         -x      -x     \                  cos (x) /    4*sin (x)|
                                                   |                     2    | |                                           2            2           4                                       2         -x                        |     /     -x      -x   2*sin(x)\ |     -x      -x   10*sin(x)   12*sin (x)|   3*|------ + 2*e   - x*e   + ---------|*|------ + 2*e   - x*e   - ------------------------------- + ---------|
                                                   \                  cos (x) / |                       /      2         -x\          cos (x)     cos (x)                              x + ------ - x*e                          |   3*|1 - e   + x*e   + --------|*|- 3*e   + x*e   + --------- + ----------|     |cos(x)                       3    | |cos(x)                                2         -x             3    |
                               4            2                                   |                       |x + ------ - x*e  |                                                               cos(x)                                |     |                     2    | |                      2           4     |     \                          cos (x) / |                                x + ------ - x*e            cos (x) |
   -x     10        -x   48*sin (x)   56*sin (x)                                \                       \    cos(x)        /                                                                                                     /     \                  cos (x) / \                   cos (x)     cos (x)  /                                          \                                    cos(x)                          /
4*e   + ------ - x*e   + ---------- + ---------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------
        cos(x)               5            3                                                                                             2         -x                                                                                                                   2         -x                                                                                  2         -x                                             
                          cos (x)      cos (x)                                                                                    x + ------ - x*e                                                                                                               x + ------ - x*e                                                                              x + ------ - x*e                                               
                                                                                                                                      cos(x)                                                                                                                         cos(x)                                                                                        cos(x)                                                     
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                            2         -x                                                                                                                                                                                                      
                                                                                                                                                                                                      x + ------ - x*e                                                                                                                                                                                                        
                                                                                                                                                                                                          cos(x)
−xe−x+48sin⁡4(x)cos⁡5(x)+56sin⁡2(x)cos⁡3(x)+10cos⁡(x)+4e−x−3(−xe−x+4sin⁡2(x)cos⁡3(x)+2cos⁡(x)+2e−x)(−xe−x+4sin⁡2(x)cos⁡3(x)+2cos⁡(x)+2e−x−2(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)2x−xe−x+2cos⁡(x))x−xe−x+2cos⁡(x)−3(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)(xe−x+12sin⁡3(x)cos⁡4(x)+10sin⁡(x)cos⁡2(x)−3e−x)x−xe−x+2cos⁡(x)−(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)(xe−x+12sin⁡3(x)cos⁡4(x)+10sin⁡(x)cos⁡2(x)−3e−x−6(−xe−x+4sin⁡2(x)cos⁡3(x)+2cos⁡(x)+2e−x)(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)x−xe−x+2cos⁡(x)+6(xe−x+2sin⁡(x)cos⁡2(x)+1−e−x)3(x−xe−x+2cos⁡(x))2)x−xe−x+2cos⁡(x)x−xe−x+2cos⁡(x)\frac{- x e^{- x} + \frac{48 \sin^{4}{\left(x \right)}}{\cos^{5}{\left(x \right)}} + \frac{56 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{10}{\cos{\left(x \right)}} + 4 e^{- x} - \frac{3 \left(- x e^{- x} + \frac{4 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2}{\cos{\left(x \right)}} + 2 e^{- x}\right) \left(- x e^{- x} + \frac{4 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2}{\cos{\left(x \right)}} + 2 e^{- x} - \frac{2 \left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right)^{2}}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}}\right)}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}} - \frac{3 \left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right) \left(x e^{- x} + \frac{12 \sin^{3}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{10 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 3 e^{- x}\right)}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}} - \frac{\left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right) \left(x e^{- x} + \frac{12 \sin^{3}{\left(x \right)}}{\cos^{4}{\left(x \right)}} + \frac{10 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} - 3 e^{- x} - \frac{6 \left(- x e^{- x} + \frac{4 \sin^{2}{\left(x \right)}}{\cos^{3}{\left(x \right)}} + \frac{2}{\cos{\left(x \right)}} + 2 e^{- x}\right) \left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right)}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}} + \frac{6 \left(x e^{- x} + \frac{2 \sin{\left(x \right)}}{\cos^{2}{\left(x \right)}} + 1 - e^{- x}\right)^{3}}{\left(x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}\right)^{2}}\right)}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}}}{x - x e^{- x} + \frac{2}{\cos{\left(x \right)}}}
Simplificar
Gráfico
Derivada de (x*exp(-x)+(2*sinx/(cos(x))^2)+1-exp(-x))/(x+2/cos(x)-x*exp(-x))
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