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Derivada de:
Derivada de i*n*x
Derivada de 3^-x
Derivada de y=6x
Derivada de 25/x
Expresiones idénticas
y=x^ ocho ^cosx
y es igual a x en el grado 8 en el grado coseno de x
y es igual a x en el grado ocho en el grado coseno de x
y=x8cosx
y=x⁸^cosx

Derivada de la función/ y=x^8/ 8^cosx/ y=x^8^cosx

Derivada de y=x^8^cosx

Solución

Ha introducido [src]

 / cos(x)\
 \8      /
x

x^{8^{\cos{\left(x \right)}}}

x^(8^cos(x))

Solución detallada

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

Perola derivada

$8^{8^{\cos{\left(x \right)}} \cos{\left(x \right)}} \left(\log{\left(8^{\cos{\left(x \right)}} \right)} + 1\right)$

Respuesta:

$8^{8^{\cos{\left(x \right)}} \cos{\left(x \right)}} \left(\log{\left(8^{\cos{\left(x \right)}} \right)} + 1\right)$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

 / cos(x)\ / cos(x)                               \
 \8      / |8          cos(x)                     |
x         *|------- - 8      *log(8)*log(x)*sin(x)|
           \   x                                  /

x^{8^{\cos{\left(x \right)}}} \left(- 8^{\cos{\left(x \right)}} \log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} + \frac{8^{\cos{\left(x \right)}}}{x}\right)

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Segunda derivada [src]

         / cos(x)\ /                                           2                                                                  \
 cos(x)  \8      / |  1     cos(x) /  1                       \       2       2                                    2*log(8)*sin(x)|
8      *x         *|- -- + 8      *|- - + log(8)*log(x)*sin(x)|  + log (8)*sin (x)*log(x) - cos(x)*log(8)*log(x) - ---------------|
                   |   2           \  x                       /                                                           x       |
                   \  x                                                                                                           /

8^{\cos{\left(x \right)}} x^{8^{\cos{\left(x \right)}}} \left(8^{\cos{\left(x \right)}} \left(\log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \frac{1}{x}\right)^{2} + \log{\left(8 \right)}^{2} \log{\left(x \right)} \sin^{2}{\left(x \right)} - \log{\left(8 \right)} \log{\left(x \right)} \cos{\left(x \right)} - \frac{2 \log{\left(8 \right)} \sin{\left(x \right)}}{x} - \frac{1}{x^{2}}\right)

Simplificar

Tercera derivada [src]

         / cos(x)\ /                                           3                                                                                                                                                                                          2       2                                                      \
 cos(x)  \8      / |2     2*cos(x) /  1                       \                              3       3             3*cos(x)*log(8)      cos(x) /  1                       \ /1                              2       2             2*log(8)*sin(x)\   3*log (8)*sin (x)   3*log(8)*sin(x)        2                        |
8      *x         *|-- - 8        *|- - + log(8)*log(x)*sin(x)|  + log(8)*log(x)*sin(x) - log (8)*sin (x)*log(x) - --------------- + 3*8      *|- - + log(8)*log(x)*sin(x)|*|-- + cos(x)*log(8)*log(x) - log (8)*sin (x)*log(x) + ---------------| + ----------------- + --------------- + 3*log (8)*cos(x)*log(x)*sin(x)|
                   | 3             \  x                       /                                                           x                    \  x                       / | 2                                                          x       |           x                   2                                       |
                   \x                                                                                                                                                       \x                                                                   /                              x                                        /

8^{\cos{\left(x \right)}} x^{8^{\cos{\left(x \right)}}} \left(- 8^{2 \cos{\left(x \right)}} \left(\log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \frac{1}{x}\right)^{3} + 3 \cdot 8^{\cos{\left(x \right)}} \left(\log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} - \frac{1}{x}\right) \left(- \log{\left(8 \right)}^{2} \log{\left(x \right)} \sin^{2}{\left(x \right)} + \log{\left(8 \right)} \log{\left(x \right)} \cos{\left(x \right)} + \frac{2 \log{\left(8 \right)} \sin{\left(x \right)}}{x} + \frac{1}{x^{2}}\right) - \log{\left(8 \right)}^{3} \log{\left(x \right)} \sin^{3}{\left(x \right)} + 3 \log{\left(8 \right)}^{2} \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \log{\left(8 \right)} \log{\left(x \right)} \sin{\left(x \right)} + \frac{3 \log{\left(8 \right)}^{2} \sin^{2}{\left(x \right)}}{x} - \frac{3 \log{\left(8 \right)} \cos{\left(x \right)}}{x} + \frac{3 \log{\left(8 \right)} \sin{\left(x \right)}}{x^{2}} + \frac{2}{x^{3}}\right)

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Gráfico

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Expresiones idénticas

Derivada de y=x^8^cosx

Gráfico:

Definida a trozos:

Solución