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y=(x^3+3)^sinx

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

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

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Solución

Ha introducido [src]
        sin(x)
/ 3    \      
\x  + 3/      
$$\left(x^{3} + 3\right)^{\sin{\left(x \right)}}$$
(x^3 + 3)^sin(x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
        sin(x) /                        2       \
/ 3    \       |          / 3    \   3*x *sin(x)|
\x  + 3/      *|cos(x)*log\x  + 3/ + -----------|
               |                         3      |
               \                        x  + 3  /
$$\left(x^{3} + 3\right)^{\sin{\left(x \right)}} \left(\frac{3 x^{2} \sin{\left(x \right)}}{x^{3} + 3} + \log{\left(x^{3} + 3 \right)} \cos{\left(x \right)}\right)$$
Segunda derivada [src]
               /                                  2                                                              \
        sin(x) |/                        2       \                            4                          2       |
/     3\       ||          /     3\   3*x *sin(x)|       /     3\          9*x *sin(x)   6*x*sin(x)   6*x *cos(x)|
\3 + x /      *||cos(x)*log\3 + x / + -----------|  - log\3 + x /*sin(x) - ----------- + ---------- + -----------|
               ||                             3  |                                  2           3             3  |
               |\                        3 + x   /                          /     3\       3 + x         3 + x   |
               \                                                            \3 + x /                             /
$$\left(x^{3} + 3\right)^{\sin{\left(x \right)}} \left(- \frac{9 x^{4} \sin{\left(x \right)}}{\left(x^{3} + 3\right)^{2}} + \frac{6 x^{2} \cos{\left(x \right)}}{x^{3} + 3} + \frac{6 x \sin{\left(x \right)}}{x^{3} + 3} + \left(\frac{3 x^{2} \sin{\left(x \right)}}{x^{3} + 3} + \log{\left(x^{3} + 3 \right)} \cos{\left(x \right)}\right)^{2} - \log{\left(x^{3} + 3 \right)} \sin{\left(x \right)}\right)$$
Tercera derivada [src]
               /                                  3                                                                                                                                                                                                              \
        sin(x) |/                        2       \                           /                        2       \ /                                     2             4       \                  3              4             2                            6       |
/     3\       ||          /     3\   3*x *sin(x)|              /     3\     |          /     3\   3*x *sin(x)| |   /     3\          6*x*sin(x)   6*x *cos(x)   9*x *sin(x)|   6*sin(x)   54*x *sin(x)   27*x *cos(x)   9*x *sin(x)   18*x*cos(x)   54*x *sin(x)|
\3 + x /      *||cos(x)*log\3 + x / + -----------|  - cos(x)*log\3 + x / - 3*|cos(x)*log\3 + x / + -----------|*|log\3 + x /*sin(x) - ---------- - ----------- + -----------| + -------- - ------------ - ------------ - ----------- + ----------- + ------------|
               ||                             3  |                           |                             3  | |                            3             3              2 |         3             2              2             3             3              3  |
               |\                        3 + x   /                           \                        3 + x   / |                       3 + x         3 + x       /     3\  |    3 + x      /     3\       /     3\         3 + x         3 + x       /     3\   |
               \                                                                                                \                                                 \3 + x /  /               \3 + x /       \3 + x /                                   \3 + x /   /
$$\left(x^{3} + 3\right)^{\sin{\left(x \right)}} \left(\frac{54 x^{6} \sin{\left(x \right)}}{\left(x^{3} + 3\right)^{3}} - \frac{27 x^{4} \cos{\left(x \right)}}{\left(x^{3} + 3\right)^{2}} - \frac{54 x^{3} \sin{\left(x \right)}}{\left(x^{3} + 3\right)^{2}} - \frac{9 x^{2} \sin{\left(x \right)}}{x^{3} + 3} + \frac{18 x \cos{\left(x \right)}}{x^{3} + 3} + \left(\frac{3 x^{2} \sin{\left(x \right)}}{x^{3} + 3} + \log{\left(x^{3} + 3 \right)} \cos{\left(x \right)}\right)^{3} - 3 \left(\frac{3 x^{2} \sin{\left(x \right)}}{x^{3} + 3} + \log{\left(x^{3} + 3 \right)} \cos{\left(x \right)}\right) \left(\frac{9 x^{4} \sin{\left(x \right)}}{\left(x^{3} + 3\right)^{2}} - \frac{6 x^{2} \cos{\left(x \right)}}{x^{3} + 3} - \frac{6 x \sin{\left(x \right)}}{x^{3} + 3} + \log{\left(x^{3} + 3 \right)} \sin{\left(x \right)}\right) - \log{\left(x^{3} + 3 \right)} \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{x^{3} + 3}\right)$$
Gráfico
Derivada de y=(x^3+3)^sinx