Sr Examen

Otras calculadoras


y=(x^3+3)^cos(x)

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

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

    Perola derivada


Respuesta:

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