Sr Examen

Derivada de x^(exp^x+6x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
  x      
 E  + 6*x
x        
xex+6xx^{e^{x} + 6 x}
x^(E^x + 6*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (ex+6x)ex+6x(log(ex+6x)+1)\left(e^{x} + 6 x\right)^{e^{x} + 6 x} \left(\log{\left(e^{x} + 6 x \right)} + 1\right)

  2. Simplificamos:

    (6x+ex)6x+ex(log(6x+ex)+1)\left(6 x + e^{x}\right)^{6 x + e^{x}} \left(\log{\left(6 x + e^{x} \right)} + 1\right)


Respuesta:

(6x+ex)6x+ex(log(6x+ex)+1)\left(6 x + e^{x}\right)^{6 x + e^{x}} \left(\log{\left(6 x + e^{x} \right)} + 1\right)

Primera derivada [src]
  x       / x                        \
 E  + 6*x |E  + 6*x   /     x\       |
x        *|-------- + \6 + E /*log(x)|
          \   x                      /
xex+6x((ex+6)log(x)+ex+6xx)x^{e^{x} + 6 x} \left(\left(e^{x} + 6\right) \log{\left(x \right)} + \frac{e^{x} + 6 x}{x}\right)
Segunda derivada [src]
          /                            2                                    \
        x |/       x                  \                       x     /     x\|
 6*x + e  ||6*x + e    /     x\       |     x          6*x + e    2*\6 + e /|
x        *||-------- + \6 + e /*log(x)|  + e *log(x) - -------- + ----------|
          |\   x                      /                    2          x     |
          \                                               x                 /
x6x+ex(((ex+6)log(x)+6x+exx)2+exlog(x)+2(ex+6)x6x+exx2)x^{6 x + e^{x}} \left(\left(\left(e^{x} + 6\right) \log{\left(x \right)} + \frac{6 x + e^{x}}{x}\right)^{2} + e^{x} \log{\left(x \right)} + \frac{2 \left(e^{x} + 6\right)}{x} - \frac{6 x + e^{x}}{x^{2}}\right)
Tercera derivada [src]
          /                            3                                                                                                                    \
        x |/       x                  \                  /     x\     /       x\      x     /       x                  \ /                   x     /     x\\|
 6*x + e  ||6*x + e    /     x\       |     x          3*\6 + e /   2*\6*x + e /   3*e      |6*x + e    /     x\       | | x          6*x + e    2*\6 + e /||
x        *||-------- + \6 + e /*log(x)|  + e *log(x) - ---------- + ------------ + ---- + 3*|-------- + \6 + e /*log(x)|*|e *log(x) - -------- + ----------||
          |\   x                      /                     2             3         x       \   x                      / |                2          x     ||
          \                                                x             x                                               \               x                 //
x6x+ex(((ex+6)log(x)+6x+exx)3+3((ex+6)log(x)+6x+exx)(exlog(x)+2(ex+6)x6x+exx2)+exlog(x)+3exx3(ex+6)x2+2(6x+ex)x3)x^{6 x + e^{x}} \left(\left(\left(e^{x} + 6\right) \log{\left(x \right)} + \frac{6 x + e^{x}}{x}\right)^{3} + 3 \left(\left(e^{x} + 6\right) \log{\left(x \right)} + \frac{6 x + e^{x}}{x}\right) \left(e^{x} \log{\left(x \right)} + \frac{2 \left(e^{x} + 6\right)}{x} - \frac{6 x + e^{x}}{x^{2}}\right) + e^{x} \log{\left(x \right)} + \frac{3 e^{x}}{x} - \frac{3 \left(e^{x} + 6\right)}{x^{2}} + \frac{2 \left(6 x + e^{x}\right)}{x^{3}}\right)