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y=(sinx)^(x^2+3)
Derivada de la función/ x^2+3/ (sinx)/ y=(sinx)^(x^2+3)

Derivada de y=(sinx)^(x^2+3)

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

Ha introducido [src] 
         2    
        x  + 3
(sin(x))
sin⁡x2+3(x)\sin^{x^{2} + 3}{\left(x \right)} 
sin(x)^(x^2 + 3)
Solución detallada

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

    Perola derivada

    (x2+3)x2+3(log⁡(x2+3)+1)\left(x^{2} + 3\right)^{x^{2} + 3} \left(\log{\left(x^{2} + 3 \right)} + 1\right)

  2. Simplificamos:

    (x2+3)x2+3(log⁡(x2+3)+1)\left(x^{2} + 3\right)^{x^{2} + 3} \left(\log{\left(x^{2} + 3 \right)} + 1\right)

Respuesta:

(x2+3)x2+3(log⁡(x2+3)+1)\left(x^{2} + 3\right)^{x^{2} + 3} \left(\log{\left(x^{2} + 3 \right)} + 1\right)

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