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y=(sin(x^(1/2)))^(ln(sin(x^(1/2))))

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  • Derivada de:
  • Derivada de x^-4/5 Derivada de x^-4/5
  • Derivada de x^2*5^x Derivada de x^2*5^x
  • Derivada de x/(1+e^x) Derivada de x/(1+e^x)
  • Derivada de u/v

  • Expresiones idénticas

  • y=(sin(x^(uno / dos)))^(ln(sin(x^(uno / dos))))
  • y es igual a ( seno de (x en el grado (1 dividir por 2))) en el grado (ln( seno de (x en el grado (1 dividir por 2))))
  • y es igual a ( seno de (x en el grado (uno dividir por dos))) en el grado (ln( seno de (x en el grado (uno dividir por dos))))
  • y=(sin(x(1/2)))(ln(sin(x(1/2))))
  • y=sinx1/2lnsinx1/2
  • y=sinx^1/2^lnsinx^1/2
  • y=(sin(x^(1 dividir por 2)))^(ln(sin(x^(1 dividir por 2))))

  • Expresiones con funciones

  • Seno sin
  • sin^2√x
  • sin(x)-5
  • sin1
  • Seno sin
  • sin^2√x
  • sin(x)-5
  • sin1
Derivada de la función/ y=(sin(x^(1/2)))^(ln(sin(x^(1/2))))

Derivada de y=(sin(x^(1/2)))^(ln(sin(x^(1/2))))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
               /   /  ___\\
            log\sin\\/ x //
/   /  ___\\               
\sin\\/ x //
sin⁡log⁡(sin⁡(x))(x)\sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)} 
sin(sqrt(x))^log(sin(sqrt(x)))
Solución detallada

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

    Perola derivada

    (log⁡(log⁡(sin⁡(x)))+1)log⁡(sin⁡(x))log⁡(sin⁡(x))\left(\log{\left(\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \right)} + 1\right) \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}

Respuesta:

(log⁡(log⁡(sin⁡(x)))+1)log⁡(sin⁡(x))log⁡(sin⁡(x))\left(\log{\left(\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \right)} + 1\right) \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}

Gráfica
02468-8-6-4-2-1010-50000000000100000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
               /   /  ___\\                           
            log\sin\\/ x //                           
/   /  ___\\                   /  ___\    /   /  ___\\
\sin\\/ x //               *cos\\/ x /*log\sin\\/ x //
------------------------------------------------------
                     ___    /  ___\                   
                   \/ x *sin\\/ x /
log⁡(sin⁡(x))sin⁡log⁡(sin⁡(x))(x)cos⁡(x)xsin⁡(x)\frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)} \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}
Simplificar
Segunda derivada [src] 
               /   /  ___\\                                                                                                                                
            log\sin\\/ x // /     /   /  ___\\        2/  ___\        2/  ___\    2/   /  ___\\      2/  ___\    /   /  ___\\      /  ___\    /   /  ___\\\
/   /  ___\\                |  log\sin\\/ x //     cos \\/ x /     cos \\/ x /*log \sin\\/ x //   cos \\/ x /*log\sin\\/ x //   cos\\/ x /*log\sin\\/ x //|
\sin\\/ x //               *|- --------------- + --------------- + ---------------------------- - --------------------------- - --------------------------|
                            |        2*x                2/  ___\               2/  ___\                        2/  ___\                3/2    /  ___\     |
                            \                    2*x*sin \\/ x /          x*sin \\/ x /                 2*x*sin \\/ x /             2*x   *sin\\/ x /     /
(log⁡(sin⁡(x))2cos⁡2(x)xsin⁡2(x)−log⁡(sin⁡(x))2x−log⁡(sin⁡(x))cos⁡2(x)2xsin⁡2(x)+cos⁡2(x)2xsin⁡2(x)−log⁡(sin⁡(x))cos⁡(x)2x32sin⁡(x))sin⁡log⁡(sin⁡(x))(x)\left(\frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{2}{\left(\sqrt{x} \right)}}{x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{2 x} - \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{\cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}
Simplificar
Tercera derivada [src] 
               /   /  ___\\                                                                                                                                                                                                                                                                                                                                             
            log\sin\\/ x // /     /   /  ___\\         2/  ___\            3/  ___\              /  ___\        3/  ___\    3/   /  ___\\      /  ___\    /   /  ___\\        3/  ___\    /   /  ___\\        2/  ___\    2/   /  ___\\        3/  ___\    2/   /  ___\\        2/   /  ___\\    /  ___\        2/  ___\    /   /  ___\\        /  ___\    /   /  ___\\\
/   /  ___\\                |3*log\sin\\/ x //    3*cos \\/ x /       3*cos \\/ x /         3*cos\\/ x /     cos \\/ x /*log \sin\\/ x //   cos\\/ x /*log\sin\\/ x //   2*cos \\/ x /*log\sin\\/ x //   3*cos \\/ x /*log \sin\\/ x //   3*cos \\/ x /*log \sin\\/ x //   3*log \sin\\/ x //*cos\\/ x /   3*cos \\/ x /*log\sin\\/ x //   3*cos\\/ x /*log\sin\\/ x //|
\sin\\/ x //               *|----------------- - ---------------- - ------------------ - ----------------- + ---------------------------- + -------------------------- + ----------------------------- - ------------------------------ - ------------------------------ - ----------------------------- + ----------------------------- + ----------------------------|
                            |          2            2    2/  ___\      3/2    3/  ___\      3/2    /  ___\          3/2    3/  ___\                3/2    /  ___\                3/2    3/  ___\                   2    2/  ___\                   3/2    3/  ___\                  3/2    /  ___\                   2    2/  ___\                 5/2    /  ___\      |
                            \       4*x          4*x *sin \\/ x /   4*x   *sin \\/ x /   4*x   *sin\\/ x /         x   *sin \\/ x /             2*x   *sin\\/ x /               x   *sin \\/ x /                2*x *sin \\/ x /                2*x   *sin \\/ x /               2*x   *sin\\/ x /                4*x *sin \\/ x /              4*x   *sin\\/ x /      /
(−3log⁡(sin⁡(x))2cos⁡2(x)2x2sin⁡2(x)+3log⁡(sin⁡(x))4x2+3log⁡(sin⁡(x))cos⁡2(x)4x2sin⁡2(x)−3cos⁡2(x)4x2sin⁡2(x)+log⁡(sin⁡(x))3cos⁡3(x)x32sin⁡3(x)−3log⁡(sin⁡(x))2cos⁡(x)2x32sin⁡(x)−3log⁡(sin⁡(x))2cos⁡3(x)2x32sin⁡3(x)+log⁡(sin⁡(x))cos⁡(x)2x32sin⁡(x)+2log⁡(sin⁡(x))cos⁡3(x)x32sin⁡3(x)−3cos⁡(x)4x32sin⁡(x)−3cos⁡3(x)4x32sin⁡3(x)+3log⁡(sin⁡(x))cos⁡(x)4x52sin⁡(x))sin⁡log⁡(sin⁡(x))(x)\left(- \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{2}{\left(\sqrt{x} \right)}}{2 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{4 x^{2}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{2}{\left(\sqrt{x} \right)}}{4 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} - \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{4 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{3} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} - \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)}^{2} \cos^{3}{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{\log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{2 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{2 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos^{3}{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} - \frac{3 \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} - \frac{3 \cos^{3}{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{3 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) \sin^{\log{\left(\sin{\left(\sqrt{x} \right)} \right)}}{\left(\sqrt{x} \right)}
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Gráfico
Derivada de y=(sin(x^(1/2)))^(ln(sin(x^(1/2))))
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