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

Derivada de y=(sin(x)^x^2)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src] 
        / 2\
        \x /
(sin(x))
sin⁡x2(x)\sin^{x^{2}}{\left(x \right)} 
sin(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
02468-8-6-4-2-1010-1010
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
        / 2\ /                   2       \
        \x / |                  x *cos(x)|
(sin(x))    *|2*x*log(sin(x)) + ---------|
             \                    sin(x) /
(x2cos⁡(x)sin⁡(x)+2xlog⁡(sin⁡(x)))sin⁡x2(x)\left(\frac{x^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 x \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{x^{2}}{\left(x \right)}
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Segunda derivada [src] 
        / 2\ /                                                    2    2    2                \
        \x / |   2                    2 /                x*cos(x)\    x *cos (x)   4*x*cos(x)|
(sin(x))    *|- x  + 2*log(sin(x)) + x *|2*log(sin(x)) + --------|  - ---------- + ----------|
             |                          \                 sin(x) /        2          sin(x)  |
             \                                                         sin (x)               /
(x2(xcos⁡(x)sin⁡(x)+2log⁡(sin⁡(x)))2−x2−x2cos⁡2(x)sin⁡2(x)+4xcos⁡(x)sin⁡(x)+2log⁡(sin⁡(x)))sin⁡x2(x)\left(x^{2} \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right)^{2} - x^{2} - \frac{x^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{4 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{x^{2}}{\left(x \right)}
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Tercera derivada [src] 
        / 2\ /                                    3                     2                                     /                      2    2                \      2    3         2       \
        \x / |        3 /                x*cos(x)\    6*cos(x)   6*x*cos (x)       /                x*cos(x)\ | 2                   x *cos (x)   4*x*cos(x)|   2*x *cos (x)   2*x *cos(x)|
(sin(x))    *|-6*x + x *|2*log(sin(x)) + --------|  + -------- - ----------- - 3*x*|2*log(sin(x)) + --------|*|x  - 2*log(sin(x)) + ---------- - ----------| + ------------ + -----------|
             |          \                 sin(x) /     sin(x)         2            \                 sin(x) / |                         2          sin(x)  |        3            sin(x)  |
             \                                                     sin (x)                                    \                      sin (x)               /     sin (x)                 /
(x3(xcos⁡(x)sin⁡(x)+2log⁡(sin⁡(x)))3+2x2cos⁡(x)sin⁡(x)+2x2cos⁡3(x)sin⁡3(x)−3x(xcos⁡(x)sin⁡(x)+2log⁡(sin⁡(x)))(x2+x2cos⁡2(x)sin⁡2(x)−4xcos⁡(x)sin⁡(x)−2log⁡(sin⁡(x)))−6x−6xcos⁡2(x)sin⁡2(x)+6cos⁡(x)sin⁡(x))sin⁡x2(x)\left(x^{3} \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right)^{3} + \frac{2 x^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 x^{2} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 3 x \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right) \left(x^{2} + \frac{x^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 2 \log{\left(\sin{\left(x \right)} \right)}\right) - 6 x - \frac{6 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{6 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{x^{2}}{\left(x \right)}
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Gráfico
Derivada de y=(sin(x)^x^2)
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