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

Derivada de y=(sinx)^x^2

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
        / 2\
        \x /
(sin(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

Respuesta:

Gráfica
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) /
$$\left(\frac{x^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 x \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{x^{2}}{\left(x \right)}$$
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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)               /
$$\left(x^{2} \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right)^{2} - x^{2} - \frac{x^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{4 x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right) \sin^{x^{2}}{\left(x \right)}$$
Simplificar
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)                 /
$$\left(x^{3} \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right)^{3} + \frac{2 x^{2} \cos{\left(x \right)}}{\sin{\left(x \right)}} + \frac{2 x^{2} \cos^{3}{\left(x \right)}}{\sin^{3}{\left(x \right)}} - 3 x \left(\frac{x \cos{\left(x \right)}}{\sin{\left(x \right)}} + 2 \log{\left(\sin{\left(x \right)} \right)}\right) \left(x^{2} + \frac{x^{2} \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} - \frac{4 x \cos{\left(x \right)}}{\sin{\left(x \right)}} - 2 \log{\left(\sin{\left(x \right)} \right)}\right) - 6 x - \frac{6 x \cos^{2}{\left(x \right)}}{\sin^{2}{\left(x \right)}} + \frac{6 \cos{\left(x \right)}}{\sin{\left(x \right)}}\right) \sin^{x^{2}}{\left(x \right)}$$
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Gráfico
Derivada de y=(sinx)^x^2
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