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y=cbrt(x)^sqrt(x)

Derivada de y=cbrt(x)^sqrt(x)

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

Ha introducido [src]
       ___
     \/ x 
3 ___     
\/ x      
(x3)x\left(\sqrt[3]{x}\right)^{\sqrt{x}}
(x^(1/3))^(sqrt(x))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    xx2(log(x)+1)x^{\frac{\sqrt{x}}{2}} \left(\log{\left(\sqrt{x} \right)} + 1\right)

  2. Simplificamos:

    xx2(log(x)+2)2\frac{x^{\frac{\sqrt{x}}{2}} \left(\log{\left(x \right)} + 2\right)}{2}


Respuesta:

xx2(log(x)+2)2\frac{x^{\frac{\sqrt{x}}{2}} \left(\log{\left(x \right)} + 2\right)}{2}

Gráfica
02468-8-6-4-2-101020-10
Primera derivada [src]
   ___                       
 \/ x                        
 ----- /             /3 ___\\
   3   |   1      log\\/ x /|
x     *|------- + ----------|
       |    ___        ___  |
       \3*\/ x     2*\/ x   /
xx3(log(x3)2x+13x)x^{\frac{\sqrt{x}}{3}} \left(\frac{\log{\left(\sqrt[3]{x} \right)}}{2 \sqrt{x}} + \frac{1}{3 \sqrt{x}}\right)
Segunda derivada [src]
   ___                                                   
 \/ x                                                    
 ----- /       /3 ___\   /         /3 ___\\             \
   3   |  9*log\\/ x /   \2 + 3*log\\/ x //*(2 + log(x))|
x     *|- ------------ + -------------------------------|
       |       3/2                      x               |
       \      x                                         /
---------------------------------------------------------
                            36                           
xx3((3log(x3)+2)(log(x)+2)x9log(x3)x32)36\frac{x^{\frac{\sqrt{x}}{3}} \left(\frac{\left(3 \log{\left(\sqrt[3]{x} \right)} + 2\right) \left(\log{\left(x \right)} + 2\right)}{x} - \frac{9 \log{\left(\sqrt[3]{x} \right)}}{x^{\frac{3}{2}}}\right)}{36}
Tercera derivada [src]
   ___                                                                                                                       
 \/ x                                                                                                                        
 ----- /               /3 ___\               2 /         /3 ___\\                      /3 ___\     /         /3 ___\\       \
   3   |   18    81*log\\/ x /   (2 + log(x)) *\2 + 3*log\\/ x //   18*(2 + log(x))*log\\/ x /   3*\2 + 3*log\\/ x //*log(x)|
x     *|- ---- + ------------- + -------------------------------- - -------------------------- - ---------------------------|
       |   5/2         5/2                      3/2                              2                             2            |
       \  x           x                        x                                x                             x             /
-----------------------------------------------------------------------------------------------------------------------------
                                                             216                                                             
xx3(3(3log(x3)+2)log(x)x218(log(x)+2)log(x3)x2+(3log(x3)+2)(log(x)+2)2x32+81log(x3)x5218x52)216\frac{x^{\frac{\sqrt{x}}{3}} \left(- \frac{3 \left(3 \log{\left(\sqrt[3]{x} \right)} + 2\right) \log{\left(x \right)}}{x^{2}} - \frac{18 \left(\log{\left(x \right)} + 2\right) \log{\left(\sqrt[3]{x} \right)}}{x^{2}} + \frac{\left(3 \log{\left(\sqrt[3]{x} \right)} + 2\right) \left(\log{\left(x \right)} + 2\right)^{2}}{x^{\frac{3}{2}}} + \frac{81 \log{\left(\sqrt[3]{x} \right)}}{x^{\frac{5}{2}}} - \frac{18}{x^{\frac{5}{2}}}\right)}{216}
Gráfico
Derivada de y=cbrt(x)^sqrt(x)