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(x+sin(6x))^(x^2)
Derivada de la función/ x+sin/ (x^2)/ sin(6x)/ (x+sin(6x))^(x^2)

Derivada de (x+sin(6x))^(x^2)

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

Gráfico:

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Solución

Ha introducido [src] 
              / 2\
              \x /
(x + sin(6*x))
(x+sin⁡(6x))x2\left(x + \sin{\left(6 x \right)}\right)^{x^{2}} 
(x + sin(6*x))^(x^2)
Solución detallada

  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log⁡(x2)+1)∣x∣2x2\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}

Respuesta:

(log⁡(x2)+1)∣x∣2x2\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}

Gráfica
02468-8-6-4-2-1010-5e991e100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
              / 2\ /                         2                 \
              \x / |                        x *(1 + 6*cos(6*x))|
(x + sin(6*x))    *|2*x*log(x + sin(6*x)) + -------------------|
                   \                            x + sin(6*x)   /
(x+sin⁡(6x))x2(x2(6cos⁡(6x)+1)x+sin⁡(6x)+2xlog⁡(x+sin⁡(6x)))\left(x + \sin{\left(6 x \right)}\right)^{x^{2}} \left(\frac{x^{2} \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 x \log{\left(x + \sin{\left(6 x \right)} \right)}\right)
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Tercera derivada [src] 
                   /                                                   /                                                       2                 3                       2       2                          \                                                                                                                                       \
                   |                                                   |                                         2            x *(1 + 6*cos(6*x))    3*x*(1 + 6*cos(6*x))    54*x *(1 + 6*cos(6*x))*sin(6*x)|                                                                                                                                       |
                   |                                                 2*|-3 - 18*cos(6*x) + 108*x*sin(6*x) + 108*x *cos(6*x) - -------------------- + --------------------- - -------------------------------|                                                                                                                                       |
              / 2\ |                                             3     |                                                                      2           x + sin(6*x)                 x + sin(6*x)         |                                                  /                        2                 2                              2         \|
              \x / | 3 /                      x*(1 + 6*cos(6*x))\      \                                                        (x + sin(6*x))                                                              /       /                      x*(1 + 6*cos(6*x))\ |                       x *(1 + 6*cos(6*x))    4*x*(1 + 6*cos(6*x))   36*x *sin(6*x)||
(x + sin(6*x))    *|x *|2*log(x + sin(6*x)) + ------------------|  - ---------------------------------------------------------------------------------------------------------------------------------------- - 3*x*|2*log(x + sin(6*x)) + ------------------|*|-2*log(x + sin(6*x)) + -------------------- - -------------------- + --------------||
                   |   \                         x + sin(6*x)   /                                                                  x + sin(6*x)                                                                     \                         x + sin(6*x)   / |                                       2          x + sin(6*x)        x + sin(6*x) ||
                   \                                                                                                                                                                                                                                           \                         (x + sin(6*x))                                            //
(x+sin⁡(6x))x2(x3(x(6cos⁡(6x)+1)x+sin⁡(6x)+2log⁡(x+sin⁡(6x)))3−3x(x(6cos⁡(6x)+1)x+sin⁡(6x)+2log⁡(x+sin⁡(6x)))(36x2sin⁡(6x)x+sin⁡(6x)+x2(6cos⁡(6x)+1)2(x+sin⁡(6x))2−4x(6cos⁡(6x)+1)x+sin⁡(6x)−2log⁡(x+sin⁡(6x)))−2(108x2cos⁡(6x)−54x2(6cos⁡(6x)+1)sin⁡(6x)x+sin⁡(6x)−x2(6cos⁡(6x)+1)3(x+sin⁡(6x))2+108xsin⁡(6x)+3x(6cos⁡(6x)+1)2x+sin⁡(6x)−18cos⁡(6x)−3)x+sin⁡(6x))\left(x + \sin{\left(6 x \right)}\right)^{x^{2}} \left(x^{3} \left(\frac{x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right)^{3} - 3 x \left(\frac{x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} + 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right) \left(\frac{36 x^{2} \sin{\left(6 x \right)}}{x + \sin{\left(6 x \right)}} + \frac{x^{2} \left(6 \cos{\left(6 x \right)} + 1\right)^{2}}{\left(x + \sin{\left(6 x \right)}\right)^{2}} - \frac{4 x \left(6 \cos{\left(6 x \right)} + 1\right)}{x + \sin{\left(6 x \right)}} - 2 \log{\left(x + \sin{\left(6 x \right)} \right)}\right) - \frac{2 \left(108 x^{2} \cos{\left(6 x \right)} - \frac{54 x^{2} \left(6 \cos{\left(6 x \right)} + 1\right) \sin{\left(6 x \right)}}{x + \sin{\left(6 x \right)}} - \frac{x^{2} \left(6 \cos{\left(6 x \right)} + 1\right)^{3}}{\left(x + \sin{\left(6 x \right)}\right)^{2}} + 108 x \sin{\left(6 x \right)} + \frac{3 x \left(6 \cos{\left(6 x \right)} + 1\right)^{2}}{x + \sin{\left(6 x \right)}} - 18 \cos{\left(6 x \right)} - 3\right)}{x + \sin{\left(6 x \right)}}\right)
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Gráfico
Derivada de (x+sin(6x))^(x^2)
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