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x^(x^2+3x)
The derivative of the function/ x^(x^2+3x)

Derivative of x^(x^2+3x)

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

The graph:

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The solution

You have entered [src] 
  2      
 x  + 3*x
x
xx2+3xx^{x^{2} + 3 x} 
  /  2      \
d | x  + 3*x|
--\x        /
dx
ddxxx2+3x\frac{d}{d x} x^{x^{2} + 3 x}
Transform
Detail solution

  1. Don't know the steps in finding this derivative.

    But the derivative is

    (x2+3x)x2+3x(log⁡(x2+3x)+1)\left(x^{2} + 3 x\right)^{x^{2} + 3 x} \left(\log{\left(x^{2} + 3 x \right)} + 1\right)

  2. Now simplify:

    (x(x+3))x(x+3)(log⁡(x(x+3))+1)\left(x \left(x + 3\right)\right)^{x \left(x + 3\right)} \left(\log{\left(x \left(x + 3\right) \right)} + 1\right)

The answer is:

(x(x+3))x(x+3)(log⁡(x(x+3))+1)\left(x \left(x + 3\right)\right)^{x \left(x + 3\right)} \left(\log{\left(x \left(x + 3\right) \right)} + 1\right)

The graph
02468-8-6-4-2-10101e132-5e131
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
  2       / 2                         \
 x  + 3*x |x  + 3*x                   |
x        *|-------- + (3 + 2*x)*log(x)|
          \   x                       /
xx2+3x((2x+3)log⁡(x)+x2+3xx)x^{x^{2} + 3 x} \left(\left(2 x + 3\right) \log{\left(x \right)} + \frac{x^{2} + 3 x}{x}\right)
Simplify
The second derivative [src] 
 x*(3 + x) /                          2              3 + x   2*(3 + 2*x)\
x         *|(3 + x + (3 + 2*x)*log(x))  + 2*log(x) - ----- + -----------|
           \                                           x          x     /
xx(x+3)(((2x+3)log⁡(x)+x+3)2+2log⁡(x)−x+3x+2⋅(2x+3)x)x^{x \left(x + 3\right)} \left(\left(\left(2 x + 3\right) \log{\left(x \right)} + x + 3\right)^{2} + 2 \log{\left(x \right)} - \frac{x + 3}{x} + \frac{2 \cdot \left(2 x + 3\right)}{x}\right)
Simplify
The third derivative [src] 
           /                                  3*(3 + 2*x)   2*(3 + x)                                                                \
           |                              6 - ----------- + ---------                                                                |
 x*(3 + x) |                          3            x            x                                    /           3 + x   2*(3 + 2*x)\|
x         *|(3 + x + (3 + 2*x)*log(x))  + --------------------------- + 3*(3 + x + (3 + 2*x)*log(x))*|2*log(x) - ----- + -----------||
           \                                           x                                             \             x          x     //
xx(x+3)(((2x+3)log⁡(x)+x+3)3+3((2x+3)log⁡(x)+x+3)(2log⁡(x)−x+3x+2⋅(2x+3)x)+6+2(x+3)x−3⋅(2x+3)xx)x^{x \left(x + 3\right)} \left(\left(\left(2 x + 3\right) \log{\left(x \right)} + x + 3\right)^{3} + 3 \left(\left(2 x + 3\right) \log{\left(x \right)} + x + 3\right) \left(2 \log{\left(x \right)} - \frac{x + 3}{x} + \frac{2 \cdot \left(2 x + 3\right)}{x}\right) + \frac{6 + \frac{2 \left(x + 3\right)}{x} - \frac{3 \cdot \left(2 x + 3\right)}{x}}{x}\right)
Simplify
The graph
Derivative of x^(x^2+3x)
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