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x*exp((2*x-5)/4)*sqrt(5*x-4-x^2)+9/4*arcsin(sqrt((x-1)/3))(-x)
Derivada de la función/ x*exp((2*x-5)/4)*sqrt(5*x-4-x^2)+9/4*arcsin(sqrt((x-1)/3))(-x)

Derivada de x*exp((2*x-5)/4)*sqrt(5*x-4-x^2)+9/4*arcsin(sqrt((x-1)/3))(-x)

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

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Solución

Ha introducido [src] 
                                     /    _______\     
   2*x - 5                           |   / x - 1 |     
   -------    ______________   9*asin|  /  ----- |     
      4      /            2          \\/     3   /     
x*e       *\/  5*x - 4 - x   + -------------------*(-x)
                                        4
−x9asin⁡(x−13)4+xe2x−54−x2+(5x−4)- x \frac{9 \operatorname{asin}{\left(\sqrt{\frac{x - 1}{3}} \right)}}{4} + x e^{\frac{2 x - 5}{4}} \sqrt{- x^{2} + \left(5 x - 4\right)} 
(x*exp((2*x - 5)/4))*sqrt(5*x - 4 - x^2) + (9*asin(sqrt((x - 1)/3))/4)*(-x)
Gráfica
02468-8-6-4-2-1010-5050
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Primera derivada [src] 
        /    _______\                     /   2*x - 5           \                2*x - 5                              
        |   / x - 1 |                     |   -------    2*x - 5|                -------                              
  9*asin|  /  ----- |      ______________ |      4       -------|                   4                     ___         
        \\/     3   /     /            2  |x*e              4   |   x*(5/2 - x)*e                   3*x*\/ 3          
- ------------------- + \/  5*x - 4 - x  *|---------- + e       | + -------------------- - ---------------------------
           4                              \    2                /       ______________           ___________          
                                                                       /            2           /     x - 1    _______
                                                                     \/  5*x - 4 - x       8*  /  1 - ----- *\/ x - 1 
                                                                                             \/         3
x(52−x)e2x−54−x2+(5x−4)−33x8x−1−x−13+1+−x2+(5x−4)(xe2x−542+e2x−54)−9asin⁡(x−13)4\frac{x \left(\frac{5}{2} - x\right) e^{\frac{2 x - 5}{4}}}{\sqrt{- x^{2} + \left(5 x - 4\right)}} - \frac{3 \sqrt{3} x}{8 \sqrt{x - 1} \sqrt{- \frac{x - 1}{3} + 1}} + \sqrt{- x^{2} + \left(5 x - 4\right)} \left(\frac{x e^{\frac{2 x - 5}{4}}}{2} + e^{\frac{2 x - 5}{4}}\right) - \frac{9 \operatorname{asin}{\left(\sqrt{\frac{x - 1}{3}} \right)}}{4}
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Segunda derivada [src] 
                                              /     5   x        5   x\            5   x                                                5   x               /     5   x        5   x\                                               5   x                   5   x
                              _______________ |   - - + -      - - + -|          - - + -                                              - - + -               |   - - + -      - - + -|                                             - - + -                 - - + -
                             /       2        |     4   2        4   2|            4   2                                                4   2               |     4   2        4   2|                                          2    4   2                   4   2
            9              \/  -4 - x  + 5*x *\4*e        + x*e       /       x*e                        9*x              (-5 + 2*x)*e           (-5 + 2*x)*\2*e        + x*e       /             9*x              x*(-5 + 2*x) *e          x*(-5 + 2*x)*e       
- ---------------------- + -------------------------------------------- - ------------------ - ------------------------ - -------------------- - ------------------------------------ + ------------------------ - ---------------------- - ---------------------
      ________   _______                        4                            _______________        ________        3/2        _______________                _______________                      3/2   _______                     3/2          _______________
  4*\/ -1 + x *\/ 4 - x                                                     /       2          16*\/ -1 + x *(4 - x)          /       2                      /       2                  16*(-1 + x)   *\/ 4 - x       /      2      \            /       2       
                                                                          \/  -4 - x  + 5*x                               2*\/  -4 - x  + 5*x            4*\/  -4 - x  + 5*x                                        4*\-4 - x  + 5*x/        4*\/  -4 - x  + 5*x
−x(2x−5)2ex2−544(−x2+5x−4)32−x(2x−5)ex2−544−x2+5x−4−xex2−54−x2+5x−4+9x164−x(x−1)32−9x16(4−x)32x−1−(2x−5)(xex2−54+2ex2−54)4−x2+5x−4−(2x−5)ex2−542−x2+5x−4+(xex2−54+4ex2−54)−x2+5x−44−944−xx−1- \frac{x \left(2 x - 5\right)^{2} e^{\frac{x}{2} - \frac{5}{4}}}{4 \left(- x^{2} + 5 x - 4\right)^{\frac{3}{2}}} - \frac{x \left(2 x - 5\right) e^{\frac{x}{2} - \frac{5}{4}}}{4 \sqrt{- x^{2} + 5 x - 4}} - \frac{x e^{\frac{x}{2} - \frac{5}{4}}}{\sqrt{- x^{2} + 5 x - 4}} + \frac{9 x}{16 \sqrt{4 - x} \left(x - 1\right)^{\frac{3}{2}}} - \frac{9 x}{16 \left(4 - x\right)^{\frac{3}{2}} \sqrt{x - 1}} - \frac{\left(2 x - 5\right) \left(x e^{\frac{x}{2} - \frac{5}{4}} + 2 e^{\frac{x}{2} - \frac{5}{4}}\right)}{4 \sqrt{- x^{2} + 5 x - 4}} - \frac{\left(2 x - 5\right) e^{\frac{x}{2} - \frac{5}{4}}}{2 \sqrt{- x^{2} + 5 x - 4}} + \frac{\left(x e^{\frac{x}{2} - \frac{5}{4}} + 4 e^{\frac{x}{2} - \frac{5}{4}}\right) \sqrt{- x^{2} + 5 x - 4}}{4} - \frac{9}{4 \sqrt{4 - x} \sqrt{x - 1}}
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Tercera derivada [src] 
           5   x                                       5   x        5   x                                       5   x                                                                            5   x                 5   x               /     5   x        5   x\               /     5   x        5   x\                                 5   x                                                 5   x                      5   x                    5   x                   5   x
         - - + -                                     - - + -      - - + -                                     - - + -                                                                          - - + -               - - + -               |   - - + -      - - + -|               |   - - + -      - - + -|      _______________          - - + -                                               - - + -                    - - + -                  - - + -                 - - + -
           4   2                                       4   2        4   2                                       4   2                                                                       2    4   2                 4   2               |     4   2        4   2|             2 |     4   2        4   2|     /       2                   4   2                                                 4   2                 3    4   2               2    4   2                   4   2
      2*e                         27              2*e        + x*e                     27                  x*e                        27*x                       27*x             (-5 + 2*x) *e          (-5 + 2*x)*e           (-5 + 2*x)*\4*e        + x*e       /   (-5 + 2*x) *\2*e        + x*e       /   \/  -4 - x  + 5*x *(6 + x)*e                     9*x              3*x*(-5 + 2*x)*e          3*x*(-5 + 2*x) *e          x*(-5 + 2*x) *e          x*(-5 + 2*x)*e       
- ------------------ - ------------------------ - ----------------------- + ------------------------ - ------------------ - ------------------------ - ------------------------ - -------------------- - -------------------- - ------------------------------------ - ------------------------------------- + ----------------------------------- + ------------------------- - ----------------------- - ------------------------ - ---------------------- - ---------------------
     _______________        ________        3/2          _______________               3/2   _______      _______________              5/2   _______        ________        5/2                    3/2        _______________                _______________                                     3/2                            8                               3/2        3/2                      3/2                       5/2                       3/2          _______________
    /       2          16*\/ -1 + x *(4 - x)            /       2           16*(-1 + x)   *\/ 4 - x      /       2          32*(-1 + x)   *\/ 4 - x    32*\/ -1 + x *(4 - x)        /      2      \          /       2                      /       2                             /      2      \                                                    16*(-1 + x)   *(4 - x)          /      2      \           /      2      \           /      2      \            /       2       
  \/  -4 - x  + 5*x                                 2*\/  -4 - x  + 5*x                                \/  -4 - x  + 5*x                                                          2*\-4 - x  + 5*x/      2*\/  -4 - x  + 5*x            4*\/  -4 - x  + 5*x                     8*\-4 - x  + 5*x/                                                                                  2*\-4 - x  + 5*x/         8*\-4 - x  + 5*x/         4*\-4 - x  + 5*x/        8*\/  -4 - x  + 5*x
−3x(2x−5)3ex2−548(−x2+5x−4)52−x(2x−5)2ex2−544(−x2+5x−4)32−x(2x−5)ex2−548−x2+5x−4−3x(2x−5)ex2−542(−x2+5x−4)32−xex2−54−x2+5x−4−27x324−x(x−1)52+9x16(4−x)32(x−1)32−27x32(4−x)52x−1+(x+6)−x2+5x−4ex2−548−(2x−5)2(xex2−54+2ex2−54)8(−x2+5x−4)32−(2x−5)2ex2−542(−x2+5x−4)32−(2x−5)(xex2−54+4ex2−54)4−x2+5x−4−(2x−5)ex2−542−x2+5x−4−xex2−54+2ex2−542−x2+5x−4−2ex2−54−x2+5x−4+27164−x(x−1)32−2716(4−x)32x−1- \frac{3 x \left(2 x - 5\right)^{3} e^{\frac{x}{2} - \frac{5}{4}}}{8 \left(- x^{2} + 5 x - 4\right)^{\frac{5}{2}}} - \frac{x \left(2 x - 5\right)^{2} e^{\frac{x}{2} - \frac{5}{4}}}{4 \left(- x^{2} + 5 x - 4\right)^{\frac{3}{2}}} - \frac{x \left(2 x - 5\right) e^{\frac{x}{2} - \frac{5}{4}}}{8 \sqrt{- x^{2} + 5 x - 4}} - \frac{3 x \left(2 x - 5\right) e^{\frac{x}{2} - \frac{5}{4}}}{2 \left(- x^{2} + 5 x - 4\right)^{\frac{3}{2}}} - \frac{x e^{\frac{x}{2} - \frac{5}{4}}}{\sqrt{- x^{2} + 5 x - 4}} - \frac{27 x}{32 \sqrt{4 - x} \left(x - 1\right)^{\frac{5}{2}}} + \frac{9 x}{16 \left(4 - x\right)^{\frac{3}{2}} \left(x - 1\right)^{\frac{3}{2}}} - \frac{27 x}{32 \left(4 - x\right)^{\frac{5}{2}} \sqrt{x - 1}} + \frac{\left(x + 6\right) \sqrt{- x^{2} + 5 x - 4} e^{\frac{x}{2} - \frac{5}{4}}}{8} - \frac{\left(2 x - 5\right)^{2} \left(x e^{\frac{x}{2} - \frac{5}{4}} + 2 e^{\frac{x}{2} - \frac{5}{4}}\right)}{8 \left(- x^{2} + 5 x - 4\right)^{\frac{3}{2}}} - \frac{\left(2 x - 5\right)^{2} e^{\frac{x}{2} - \frac{5}{4}}}{2 \left(- x^{2} + 5 x - 4\right)^{\frac{3}{2}}} - \frac{\left(2 x - 5\right) \left(x e^{\frac{x}{2} - \frac{5}{4}} + 4 e^{\frac{x}{2} - \frac{5}{4}}\right)}{4 \sqrt{- x^{2} + 5 x - 4}} - \frac{\left(2 x - 5\right) e^{\frac{x}{2} - \frac{5}{4}}}{2 \sqrt{- x^{2} + 5 x - 4}} - \frac{x e^{\frac{x}{2} - \frac{5}{4}} + 2 e^{\frac{x}{2} - \frac{5}{4}}}{2 \sqrt{- x^{2} + 5 x - 4}} - \frac{2 e^{\frac{x}{2} - \frac{5}{4}}}{\sqrt{- x^{2} + 5 x - 4}} + \frac{27}{16 \sqrt{4 - x} \left(x - 1\right)^{\frac{3}{2}}} - \frac{27}{16 \left(4 - x\right)^{\frac{3}{2}} \sqrt{x - 1}}
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Gráfico
Derivada de x*exp((2*x-5)/4)*sqrt(5*x-4-x^2)+9/4*arcsin(sqrt((x-1)/3))(-x)
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