Derivative of x^(2*x)

The solution

You have entered [src]

 2*x
x

$$x^{2 x}$$

x^(2*x)

Detail solution

Don't know the steps in finding this derivative.

But the derivative is

$\left(2 x\right)^{2 x} \left(\log{\left(2 x \right)} + 1\right)$

The answer is:

$\left(2 x\right)^{2 x} \left(\log{\left(2 x \right)} + 1\right)$

The graph

Plot the graph f(x)

Plot the graph f'(x)

The first derivative [src]

 2*x               
x   *(2 + 2*log(x))

$$x^{2 x} \left(2 \log{\left(x \right)} + 2\right)$$

Simplify

The second derivative [src]

   2*x /1                 2\
2*x   *|- + 2*(1 + log(x)) |
       \x                  /

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

Simplify

The third derivative [src]

   2*x /  1                  3   6*(1 + log(x))\
2*x   *|- -- + 4*(1 + log(x))  + --------------|
       |   2                           x       |
       \  x                                    /

$$2 x^{2 x} \left(4 \left(\log{\left(x \right)} + 1\right)^{3} + \frac{6 \left(\log{\left(x \right)} + 1\right)}{x} - \frac{1}{x^{2}}\right)$$

Simplify

The graph

Other calculators

How to use it?

Identical expressions

Similar expressions

Derivative of x^(2*x)

The graph:

Piecewise:

The solution