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x^(x^2)

Derivative of x^(x^2)

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src]
 / 2\
 \x /
x    
xx2x^{x^{2}}
x^(x^2)
Detail solution
  1. Don't know the steps in finding this derivative.

    But the derivative is

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


The answer is:

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

The graph
02468-8-6-4-2-1010-5e10110e101
The first derivative [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)
The second derivative [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)
The third derivative [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)
The graph
Derivative of x^(x^2)