Sr Examen

Otras calculadoras

Derivada de la función/ x*exp(e^x+e^(2x))/(|x|)(-x)

Derivada de x*exp(e^x+e^(2x))/(|x|)(-x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    x    2*x     
   E  + E        
x*e              
------------*(-x)
    |x|
−xxeex+e2x∣x∣- x \frac{x e^{e^{x} + e^{2 x}}}{\left|{x}\right|} 
((x*exp(E^x + E^(2*x)))/|x|)*(-x)
Primera derivada [src] 
    /                  x    2*x     x    2*x     x    2*x        \       x    2*x
    |  / x      2*x\  E  + E       E  + E       E  + E           |      E  + E   
    |x*\E  + 2*e   /*e          + e            e         *sign(x)|   x*e         
- x*|--------------------------------------- - ------------------| - ------------
    \                  |x|                             x         /       |x|
−x(x(ex+2e2x)eex+e2x+eex+e2x∣x∣−eex+e2xsign⁡(x)x)−xeex+e2x∣x∣- x \left(\frac{x \left(e^{x} + 2 e^{2 x}\right) e^{e^{x} + e^{2 x}} + e^{e^{x} + e^{2 x}}}{\left|{x}\right|} - \frac{e^{e^{x} + e^{2 x}} \operatorname{sign}{\left(x \right)}}{x}\right) - \frac{x e^{e^{x} + e^{2 x}}}{\left|{x}\right|}
Simplificar
Segunda derivada [src] 
/  /  /  sign(x)                \   /             /                     2   \\                                     \                                      \             
|  |2*|- ------- + DiracDelta(x)|   |       x     |       x   /       x\   x||  x     /      /       x\  x\        |     /      /       x\  x\            |  /     x\  x
|  |  \     x                   /   \2 + 4*e  + x*\1 + 4*e  + \1 + 2*e / *e //*e    2*\1 + x*\1 + 2*e /*e /*sign(x)|   2*\1 + x*\1 + 2*e /*e /   2*sign(x)|  \1 + e /*e 
|x*|----------------------------- - --------------------------------------------- + -------------------------------| - ----------------------- + ---------|*e           
|  |              x                                      |x|                                        2              |             |x|                 x    |             
\  \                                                                                               x               /                                      /
(x(−(x((2ex+1)2ex+4ex+1)+4ex+2)ex∣x∣+2(δ(x)−sign⁡(x)x)x+2(x(2ex+1)ex+1)sign⁡(x)x2)−2(x(2ex+1)ex+1)∣x∣+2sign⁡(x)x)e(ex+1)ex\left(x \left(- \frac{\left(x \left(\left(2 e^{x} + 1\right)^{2} e^{x} + 4 e^{x} + 1\right) + 4 e^{x} + 2\right) e^{x}}{\left|{x}\right|} + \frac{2 \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{x} + \frac{2 \left(x \left(2 e^{x} + 1\right) e^{x} + 1\right) \operatorname{sign}{\left(x \right)}}{x^{2}}\right) - \frac{2 \left(x \left(2 e^{x} + 1\right) e^{x} + 1\right)}{\left|{x}\right|} + \frac{2 \operatorname{sign}{\left(x \right)}}{x}\right) e^{\left(e^{x} + 1\right) e^{x}}
Simplificar
Tercera derivada [src] 
/  /  /  4*DiracDelta(x)   3*sign(x)                   \                                                                                                                                                                                                                   \                                                                                                                    \             
|  |2*|- --------------- + --------- + DiracDelta(x, 1)|   /              /                     3                                  \               2   \        /      /       x\  x\ /  sign(x)                \     /             /                     2   \\           |     /  sign(x)                \     /             /                     2   \\                                     |             
|  |  |         x               2                      |   |        x     |       x   /       x\   2*x     /       x\ /       x\  x|     /       x\   x|  x   6*\1 + x*\1 + 2*e /*e /*|- ------- + DiracDelta(x)|     |       x     |       x   /       x\   x||  x        |   6*|- ------- + DiracDelta(x)|     |       x     |       x   /       x\   x||  x     /      /       x\  x\        |  /     x\  x
|  |  \                        x                       /   \3 + 12*e  + x*\1 + 8*e  + \1 + 2*e / *e    + 3*\1 + 2*e /*\1 + 4*e /*e / + 3*\1 + 2*e / *e /*e                            \     x                   /   3*\2 + 4*e  + x*\1 + 4*e  + \1 + 2*e / *e //*e *sign(x)|     \     x                   /   3*\2 + 4*e  + x*\1 + 4*e  + \1 + 2*e / *e //*e    6*\1 + x*\1 + 2*e /*e /*sign(x)|  \1 + e /*e 
|x*|---------------------------------------------------- - ------------------------------------------------------------------------------------------------ + --------------------------------------------------- + -------------------------------------------------------| + ----------------------------- - ----------------------------------------------- + -------------------------------|*e           
|  |                         x                                                                           |x|                                                                            2                                                       2                          |                 x                                       |x|                                         2              |             
\  \                                                                                                                                                                                   x                                                       x                           /                                                                                                    x               /
(x(−(x((2ex+1)3e2x+3(2ex+1)(4ex+1)ex+8ex+1)+3(2ex+1)2ex+12ex+3)ex∣x∣+2(δ(1)(x)−4δ(x)x+3sign⁡(x)x2)x+6(x(2ex+1)ex+1)(δ(x)−sign⁡(x)x)x2+3(x((2ex+1)2ex+4ex+1)+4ex+2)exsign⁡(x)x2)−3(x((2ex+1)2ex+4ex+1)+4ex+2)ex∣x∣+6(δ(x)−sign⁡(x)x)x+6(x(2ex+1)ex+1)sign⁡(x)x2)e(ex+1)ex\left(x \left(- \frac{\left(x \left(\left(2 e^{x} + 1\right)^{3} e^{2 x} + 3 \left(2 e^{x} + 1\right) \left(4 e^{x} + 1\right) e^{x} + 8 e^{x} + 1\right) + 3 \left(2 e^{x} + 1\right)^{2} e^{x} + 12 e^{x} + 3\right) e^{x}}{\left|{x}\right|} + \frac{2 \left(\delta^{\left( 1 \right)}\left( x \right) - \frac{4 \delta\left(x\right)}{x} + \frac{3 \operatorname{sign}{\left(x \right)}}{x^{2}}\right)}{x} + \frac{6 \left(x \left(2 e^{x} + 1\right) e^{x} + 1\right) \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{x^{2}} + \frac{3 \left(x \left(\left(2 e^{x} + 1\right)^{2} e^{x} + 4 e^{x} + 1\right) + 4 e^{x} + 2\right) e^{x} \operatorname{sign}{\left(x \right)}}{x^{2}}\right) - \frac{3 \left(x \left(\left(2 e^{x} + 1\right)^{2} e^{x} + 4 e^{x} + 1\right) + 4 e^{x} + 2\right) e^{x}}{\left|{x}\right|} + \frac{6 \left(\delta\left(x\right) - \frac{\operatorname{sign}{\left(x \right)}}{x}\right)}{x} + \frac{6 \left(x \left(2 e^{x} + 1\right) e^{x} + 1\right) \operatorname{sign}{\left(x \right)}}{x^{2}}\right) e^{\left(e^{x} + 1\right) e^{x}}
Simplificar
    © Sr Examen – Калькулятор