Sr Examen

Derivada de (x)^x^2

Función f() - derivada -er orden en el punto
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Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
 / 2\
 \x /
x    
xx2x^{x^{2}}
x^(x^2)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

    (log(x2)+1)x2x2\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}


Respuesta:

(log(x2)+1)x2x2\left(\log{\left(x^{2} \right)} + 1\right) \left|{x}\right|^{2 x^{2}}

Gráfica
02468-8-6-4-2-1010-5e10110e101
Primera derivada [src]
 / 2\                 
 \x /                 
x    *(x + 2*x*log(x))
xx2(2xlog(x)+x)x^{x^{2}} \left(2 x \log{\left(x \right)} + x\right)
Segunda derivada [src]
 / 2\                                    
 \x / /                2               2\
x    *\3 + 2*log(x) + x *(1 + 2*log(x)) /
xx2(x2(2log(x)+1)2+2log(x)+3)x^{x^{2}} \left(x^{2} \left(2 \log{\left(x \right)} + 1\right)^{2} + 2 \log{\left(x \right)} + 3\right)
3-я производная [src]
 / 2\                                                             
 \x / /2    3               3                                    \
x    *|- + x *(1 + 2*log(x))  + 3*x*(1 + 2*log(x))*(3 + 2*log(x))|
      \x                                                         /
xx2(x3(2log(x)+1)3+3x(2log(x)+1)(2log(x)+3)+2x)x^{x^{2}} \left(x^{3} \left(2 \log{\left(x \right)} + 1\right)^{3} + 3 x \left(2 \log{\left(x \right)} + 1\right) \left(2 \log{\left(x \right)} + 3\right) + \frac{2}{x}\right)
Tercera derivada [src]
 / 2\                                                             
 \x / /2    3               3                                    \
x    *|- + x *(1 + 2*log(x))  + 3*x*(1 + 2*log(x))*(3 + 2*log(x))|
      \x                                                         /
xx2(x3(2log(x)+1)3+3x(2log(x)+1)(2log(x)+3)+2x)x^{x^{2}} \left(x^{3} \left(2 \log{\left(x \right)} + 1\right)^{3} + 3 x \left(2 \log{\left(x \right)} + 1\right) \left(2 \log{\left(x \right)} + 3\right) + \frac{2}{x}\right)
Gráfico
Derivada de (x)^x^2