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y=ln*arcsin(e^x^2)
Derivada de la función/ e^x^2/ arcsin/ y=ln*arcsin(e^x^2)

Derivada de y=ln*arcsin(e^x^2)

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

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Solución

Ha introducido [src] 
           / / 2\\
           | \x /|
log(x)*asin\E    /
log⁡(x)asin⁡(ex2)\log{\left(x \right)} \operatorname{asin}{\left(e^{x^{2}} \right)} 
log(x)*asin(E^(x^2))
Gráfica
02468-8-6-4-2-10100.02-0.02
Trazar el gráfico f(x)
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Primera derivada [src] 
    / / 2\\        / 2\       
    | \x /|        \x /       
asin\E    /   2*x*e    *log(x)
----------- + ----------------
     x            ___________ 
                 /         2  
                /       2*x   
              \/   1 - e
2xex2log⁡(x)1−e2x2+asin⁡(ex2)x\frac{2 x e^{x^{2}} \log{\left(x \right)}}{\sqrt{1 - e^{2 x^{2}}}} + \frac{\operatorname{asin}{\left(e^{x^{2}} \right)}}{x}
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Segunda derivada [src] 
                                    /                    2\             
                                    |              2  2*x |  / 2\       
                                    |       2   2*x *e    |  \x /       
                                  2*|1 + 2*x  - ----------|*e    *log(x)
      / / 2\\          / 2\         |                    2|             
      | \x /|          \x /         |                 2*x |             
  asin\E    /       4*e             \           -1 + e    /             
- ----------- + --------------- + --------------------------------------
        2           ___________                  ___________            
       x           /         2                  /         2             
                  /       2*x                  /       2*x              
                \/   1 - e                   \/   1 - e
2(2x2−2x2e2x2e2x2−1+1)ex2log⁡(x)1−e2x2+4ex21−e2x2−asin⁡(ex2)x2\frac{2 \left(2 x^{2} - \frac{2 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + 1\right) e^{x^{2}} \log{\left(x \right)}}{\sqrt{1 - e^{2 x^{2}}}} + \frac{4 e^{x^{2}}}{\sqrt{1 - e^{2 x^{2}}}} - \frac{\operatorname{asin}{\left(e^{x^{2}} \right)}}{x^{2}}
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4-я производная [src] 
  /                                         /                  2              2              2 \                                             /                          2                2              2             2              2                2\             \
  |                                         |               2*x         2  2*x         2  4*x  |  / 2\     /                    2\           |                       2*x           4  6*x         4  2*x        2  2*x         2  4*x           4  4*x |  / 2\       |
  |                                         |       2    3*e         8*x *e         6*x *e     |  \x /     |              2  2*x |  / 2\     |       4       2    3*e          60*x *e        52*x *e       48*x *e        36*x *e         108*x *e    |  \x /       |
  |                                       8*|3 + 2*x  - ---------- - ---------- + -------------|*e         |       2   2*x *e    |  \x /   2*|3 + 4*x  + 12*x  - ---------- - ------------- - ----------- - ----------- + ------------- + -------------|*e    *log(x)|
  |                                         |                    2            2               2|         6*|1 + 2*x  - ----------|*e         |                            2               3             2             2               2               2|             |
  |        / / 2\\           / 2\           |                 2*x          2*x    /         2\ |           |                    2|           |                         2*x    /         2\           2*x           2*x    /         2\    /         2\ |             |
  |        | \x /|           \x /           |           -1 + e       -1 + e       |      2*x | |           |                 2*x |           |                   -1 + e       |      2*x |     -1 + e        -1 + e       |      2*x |    |      2*x | |             |
  |  3*asin\E    /        8*e               \                                     \-1 + e    / /           \           -1 + e    /           \                                \-1 + e    /                                \-1 + e    /    \-1 + e    / /             |
2*|- ------------- + ------------------ + ------------------------------------------------------------ - ------------------------------- + --------------------------------------------------------------------------------------------------------------------------|
  |         4               ___________                             ___________                                        ___________                                                                  ___________                                                      |
  |        x               /         2                             /         2                                        /         2                                                                  /         2                                                       |
  |                   2   /       2*x                             /       2*x                                    2   /       2*x                                                                  /       2*x                                                        |
  \                  x *\/   1 - e                              \/   1 - e                                      x *\/   1 - e                                                                   \/   1 - e                                                           /
2(8(2x2−8x2e2x2e2x2−1+6x2e4x2(e2x2−1)2+3−3e2x2e2x2−1)ex21−e2x2+2(4x4−52x4e2x2e2x2−1+108x4e4x2(e2x2−1)2−60x4e6x2(e2x2−1)3+12x2−48x2e2x2e2x2−1+36x2e4x2(e2x2−1)2+3−3e2x2e2x2−1)ex2log⁡(x)1−e2x2−6(2x2−2x2e2x2e2x2−1+1)ex2x21−e2x2+8ex2x21−e2x2−3asin⁡(ex2)x4)2 \left(\frac{8 \left(2 x^{2} - \frac{8 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + \frac{6 x^{2} e^{4 x^{2}}}{\left(e^{2 x^{2}} - 1\right)^{2}} + 3 - \frac{3 e^{2 x^{2}}}{e^{2 x^{2}} - 1}\right) e^{x^{2}}}{\sqrt{1 - e^{2 x^{2}}}} + \frac{2 \left(4 x^{4} - \frac{52 x^{4} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + \frac{108 x^{4} e^{4 x^{2}}}{\left(e^{2 x^{2}} - 1\right)^{2}} - \frac{60 x^{4} e^{6 x^{2}}}{\left(e^{2 x^{2}} - 1\right)^{3}} + 12 x^{2} - \frac{48 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + \frac{36 x^{2} e^{4 x^{2}}}{\left(e^{2 x^{2}} - 1\right)^{2}} + 3 - \frac{3 e^{2 x^{2}}}{e^{2 x^{2}} - 1}\right) e^{x^{2}} \log{\left(x \right)}}{\sqrt{1 - e^{2 x^{2}}}} - \frac{6 \left(2 x^{2} - \frac{2 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + 1\right) e^{x^{2}}}{x^{2} \sqrt{1 - e^{2 x^{2}}}} + \frac{8 e^{x^{2}}}{x^{2} \sqrt{1 - e^{2 x^{2}}}} - \frac{3 \operatorname{asin}{\left(e^{x^{2}} \right)}}{x^{4}}\right)
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Tercera derivada [src] 
  /                                                                        /                  2              2              2 \             \
  |                                    /                    2\             |               2*x         2  2*x         2  4*x  |  / 2\       |
  |                                    |              2  2*x |  / 2\       |       2    3*e         8*x *e         6*x *e     |  \x /       |
  |                                    |       2   2*x *e    |  \x /   2*x*|3 + 2*x  - ---------- - ---------- + -------------|*e    *log(x)|
  |                                  3*|1 + 2*x  - ----------|*e           |                    2            2               2|             |
  |    / / 2\\           / 2\          |                    2|             |                 2*x          2*x    /         2\ |             |
  |    | \x /|           \x /          |                 2*x |             |           -1 + e       -1 + e       |      2*x | |             |
  |asin\E    /        3*e              \           -1 + e    /             \                                     \-1 + e    / /             |
2*|----------- - ----------------- + ------------------------------- + ---------------------------------------------------------------------|
  |      3             ___________                ___________                                         ___________                           |
  |     x             /         2                /         2                                         /         2                            |
  |                  /       2*x                /       2*x                                         /       2*x                             |
  \              x*\/   1 - e               x*\/   1 - e                                          \/   1 - e                                /
2(2x(2x2−8x2e2x2e2x2−1+6x2e4x2(e2x2−1)2+3−3e2x2e2x2−1)ex2log⁡(x)1−e2x2+3(2x2−2x2e2x2e2x2−1+1)ex2x1−e2x2−3ex2x1−e2x2+asin⁡(ex2)x3)2 \left(\frac{2 x \left(2 x^{2} - \frac{8 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + \frac{6 x^{2} e^{4 x^{2}}}{\left(e^{2 x^{2}} - 1\right)^{2}} + 3 - \frac{3 e^{2 x^{2}}}{e^{2 x^{2}} - 1}\right) e^{x^{2}} \log{\left(x \right)}}{\sqrt{1 - e^{2 x^{2}}}} + \frac{3 \left(2 x^{2} - \frac{2 x^{2} e^{2 x^{2}}}{e^{2 x^{2}} - 1} + 1\right) e^{x^{2}}}{x \sqrt{1 - e^{2 x^{2}}}} - \frac{3 e^{x^{2}}}{x \sqrt{1 - e^{2 x^{2}}}} + \frac{\operatorname{asin}{\left(e^{x^{2}} \right)}}{x^{3}}\right)
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Gráfico
Derivada de y=ln*arcsin(e^x^2)
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