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

Derivada de x^sin(x^2)

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

Gráfico:

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Definida a trozos:

Solución

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

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

    Perola derivada

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

Respuesta:

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

Gráfica
02468-8-6-4-2-1010-200200
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Primera derivada [src] 
    / 2\ /   / 2\                     \
 sin\x / |sin\x /          / 2\       |
x       *|------- + 2*x*cos\x /*log(x)|
         \   x                        /
xsin⁡(x2)(2xlog⁡(x)cos⁡(x2)+sin⁡(x2)x)x^{\sin{\left(x^{2} \right)}} \left(2 x \log{\left(x \right)} \cos{\left(x^{2} \right)} + \frac{\sin{\left(x^{2} \right)}}{x}\right)
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Segunda derivada [src] 
         /                              2                                                               \
    / 2\ |/   / 2\                     \                   / 2\                                         |
 sin\x / ||sin\x /          / 2\       |         / 2\   sin\x /        / 2\             2           / 2\|
x       *||------- + 2*x*cos\x /*log(x)|  + 4*cos\x / - ------- + 2*cos\x /*log(x) - 4*x *log(x)*sin\x /|
         |\   x                        /                    2                                           |
         \                                                 x                                            /
xsin⁡(x2)(−4x2log⁡(x)sin⁡(x2)+(2xlog⁡(x)cos⁡(x2)+sin⁡(x2)x)2+2log⁡(x)cos⁡(x2)+4cos⁡(x2)−sin⁡(x2)x2)x^{\sin{\left(x^{2} \right)}} \left(- 4 x^{2} \log{\left(x \right)} \sin{\left(x^{2} \right)} + \left(2 x \log{\left(x \right)} \cos{\left(x^{2} \right)} + \frac{\sin{\left(x^{2} \right)}}{x}\right)^{2} + 2 \log{\left(x \right)} \cos{\left(x^{2} \right)} + 4 \cos{\left(x^{2} \right)} - \frac{\sin{\left(x^{2} \right)}}{x^{2}}\right)
Simplificar
Tercera derivada [src] 
         /                              3                                                                                                                                                                           \
    / 2\ |/   / 2\                     \                     /   / 2\                     \ /                 / 2\                                         \        / 2\                                            |
 sin\x / ||sin\x /          / 2\       |            / 2\     |sin\x /          / 2\       | |       / 2\   sin\x /        / 2\             2           / 2\|   2*sin\x /                  / 2\      3    / 2\       |
x       *||------- + 2*x*cos\x /*log(x)|  - 12*x*sin\x / - 3*|------- + 2*x*cos\x /*log(x)|*|- 4*cos\x / + ------- - 2*cos\x /*log(x) + 4*x *log(x)*sin\x /| + --------- - 12*x*log(x)*sin\x / - 8*x *cos\x /*log(x)|
         |\   x                        /                     \   x                        / |                  2                                           |        3                                               |
         \                                                                                  \                 x                                            /       x                                                /
xsin⁡(x2)(−8x3log⁡(x)cos⁡(x2)−12xlog⁡(x)sin⁡(x2)−12xsin⁡(x2)+(2xlog⁡(x)cos⁡(x2)+sin⁡(x2)x)3−3(2xlog⁡(x)cos⁡(x2)+sin⁡(x2)x)(4x2log⁡(x)sin⁡(x2)−2log⁡(x)cos⁡(x2)−4cos⁡(x2)+sin⁡(x2)x2)+2sin⁡(x2)x3)x^{\sin{\left(x^{2} \right)}} \left(- 8 x^{3} \log{\left(x \right)} \cos{\left(x^{2} \right)} - 12 x \log{\left(x \right)} \sin{\left(x^{2} \right)} - 12 x \sin{\left(x^{2} \right)} + \left(2 x \log{\left(x \right)} \cos{\left(x^{2} \right)} + \frac{\sin{\left(x^{2} \right)}}{x}\right)^{3} - 3 \left(2 x \log{\left(x \right)} \cos{\left(x^{2} \right)} + \frac{\sin{\left(x^{2} \right)}}{x}\right) \left(4 x^{2} \log{\left(x \right)} \sin{\left(x^{2} \right)} - 2 \log{\left(x \right)} \cos{\left(x^{2} \right)} - 4 \cos{\left(x^{2} \right)} + \frac{\sin{\left(x^{2} \right)}}{x^{2}}\right) + \frac{2 \sin{\left(x^{2} \right)}}{x^{3}}\right)
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Gráfico
Derivada de x^sin(x^2)
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