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(x)^(sin(ln(x)))
Derivada de la función/ ln(x)/ (x)^(sin(ln(x)))

Derivada de (x)^(sin(ln(x)))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
 sin(log(x))
x
$$x^{\sin{\left(\log{\left(x \right)} \right)}}$$ 
x^sin(log(x))
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] 
 sin(log(x)) /sin(log(x))   cos(log(x))*log(x)\
x           *|----------- + ------------------|
             \     x                x         /
$$x^{\sin{\left(\log{\left(x \right)} \right)}} \left(\frac{\log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)}}{x} + \frac{\sin{\left(\log{\left(x \right)} \right)}}{x}\right)$$
Simplificar
Segunda derivada [src] 
 sin(log(x)) /                                  2                                                                        \
x           *\(cos(log(x))*log(x) + sin(log(x)))  - sin(log(x)) + 2*cos(log(x)) - cos(log(x))*log(x) - log(x)*sin(log(x))/
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                                                             2                                                            
                                                            x
$$\frac{x^{\sin{\left(\log{\left(x \right)} \right)}} \left(\left(\log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)} + \sin{\left(\log{\left(x \right)} \right)}\right)^{2} - \log{\left(x \right)} \sin{\left(\log{\left(x \right)} \right)} - \log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)} - \sin{\left(\log{\left(x \right)} \right)} + 2 \cos{\left(\log{\left(x \right)} \right)}\right)}{x^{2}}$$
Simplificar
Tercera derivada [src] 
 sin(log(x)) /                                  3                                                                                                                                                                                          \
x           *\(cos(log(x))*log(x) + sin(log(x)))  - sin(log(x)) - 6*cos(log(x)) + cos(log(x))*log(x) - 3*(cos(log(x))*log(x) + sin(log(x)))*(-2*cos(log(x)) + cos(log(x))*log(x) + log(x)*sin(log(x)) + sin(log(x))) + 3*log(x)*sin(log(x))/
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                                                                                                                     x
$$\frac{x^{\sin{\left(\log{\left(x \right)} \right)}} \left(\left(\log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)} + \sin{\left(\log{\left(x \right)} \right)}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)} + \sin{\left(\log{\left(x \right)} \right)}\right) \left(\log{\left(x \right)} \sin{\left(\log{\left(x \right)} \right)} + \log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)} + \sin{\left(\log{\left(x \right)} \right)} - 2 \cos{\left(\log{\left(x \right)} \right)}\right) + 3 \log{\left(x \right)} \sin{\left(\log{\left(x \right)} \right)} + \log{\left(x \right)} \cos{\left(\log{\left(x \right)} \right)} - \sin{\left(\log{\left(x \right)} \right)} - 6 \cos{\left(\log{\left(x \right)} \right)}\right)}{x^{3}}$$
Simplificar
Gráfico
Derivada de (x)^(sin(ln(x)))
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