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Derivative of x^(2x^2-3x-5)

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

The graph:

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Piecewise:

The solution

You have entered [src]
    2          
 2*x  - 3*x - 5
x              
$$x^{\left(2 x^{2} - 3 x\right) - 5}$$
x^(2*x^2 - 3*x - 5)
Detail solution
  1. Don't know the steps in finding this derivative.

    But the derivative is

  2. Now simplify:


The answer is:

The graph
The first derivative [src]
    2           /   2                              \
 2*x  - 3*x - 5 |2*x  - 3*x - 5                    |
x              *|-------------- + (-3 + 4*x)*log(x)|
                \      x                           /
$$x^{\left(2 x^{2} - 3 x\right) - 5} \left(\left(4 x - 3\right) \log{\left(x \right)} + \frac{\left(2 x^{2} - 3 x\right) - 5}{x}\right)$$
The second derivative [src]
                 /                                    2                                           \
               2 |/                           2      \                      2                     |
 -5 - 3*x + 2*x  ||                    5 - 2*x  + 3*x|               5 - 2*x  + 3*x   2*(-3 + 4*x)|
x               *||(-3 + 4*x)*log(x) - --------------|  + 4*log(x) + -------------- + ------------|
                 |\                          x       /                      2              x      |
                 \                                                         x                      /
$$x^{2 x^{2} - 3 x - 5} \left(\left(\left(4 x - 3\right) \log{\left(x \right)} - \frac{- 2 x^{2} + 3 x + 5}{x}\right)^{2} + 4 \log{\left(x \right)} + \frac{2 \left(4 x - 3\right)}{x} + \frac{- 2 x^{2} + 3 x + 5}{x^{2}}\right)$$
The third derivative [src]
                 /                                                /       2      \                                                                                                   \
                 |                                              2*\5 - 2*x  + 3*x/   3*(-3 + 4*x)                                                                                    |
                 |                                    3   -12 + ------------------ + ------------                                                                                    |
               2 |/                           2      \                   2                x           /                           2      \ /                  2                     \|
 -5 - 3*x + 2*x  ||                    5 - 2*x  + 3*x|                  x                             |                    5 - 2*x  + 3*x| |           5 - 2*x  + 3*x   2*(-3 + 4*x)||
x               *||(-3 + 4*x)*log(x) - --------------|  - --------------------------------------- + 3*|(-3 + 4*x)*log(x) - --------------|*|4*log(x) + -------------- + ------------||
                 |\                          x       /                       x                        \                          x       / |                  2              x      ||
                 \                                                                                                                         \                 x                      //
$$x^{2 x^{2} - 3 x - 5} \left(\left(\left(4 x - 3\right) \log{\left(x \right)} - \frac{- 2 x^{2} + 3 x + 5}{x}\right)^{3} + 3 \left(\left(4 x - 3\right) \log{\left(x \right)} - \frac{- 2 x^{2} + 3 x + 5}{x}\right) \left(4 \log{\left(x \right)} + \frac{2 \left(4 x - 3\right)}{x} + \frac{- 2 x^{2} + 3 x + 5}{x^{2}}\right) - \frac{-12 + \frac{3 \left(4 x - 3\right)}{x} + \frac{2 \left(- 2 x^{2} + 3 x + 5\right)}{x^{2}}}{x}\right)$$