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Derivada de y=e^3^x^2+ctg7x-arcsin2x

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src]
 / / 2\\                       
 | \x /|                       
 \3    /                       
E        + cot(7*x) - asin(2*x)
$$\left(e^{3^{x^{2}}} + \cot{\left(7 x \right)}\right) - \operatorname{asin}{\left(2 x \right)}$$
E^(3^(x^2)) + cot(7*x) - asin(2*x)
Primera derivada [src]
                                              / / 2\\       
                                        / 2\  | \x /|       
          2              2              \x /  \3    /       
-7 - 7*cot (7*x) - ------------- + 2*x*3    *e       *log(3)
                      __________                            
                     /        2                             
                   \/  1 - 4*x                              
$$2 \cdot 3^{x^{2}} x e^{3^{x^{2}}} \log{\left(3 \right)} - 7 \cot^{2}{\left(7 x \right)} - 7 - \frac{2}{\sqrt{1 - 4 x^{2}}}$$
Segunda derivada [src]
  /                                                       / / 2\\                              / / 2\\                       / / 2\\\
  |                                                 / 2\  | \x /|             / 2\             | \x /|         2             | \x /||
  |       4*x           /       2     \             \x /  \3    /             \x /  2    2     \3    /      2*x   2    2     \3    /|
2*|- ------------- + 49*\1 + cot (7*x)/*cot(7*x) + 3    *e       *log(3) + 2*3    *x *log (3)*e        + 2*3    *x *log (3)*e       |
  |            3/2                                                                                                                  |
  |  /       2\                                                                                                                     |
  \  \1 - 4*x /                                                                                                                     /
$$2 \left(2 \cdot 3^{2 x^{2}} x^{2} e^{3^{x^{2}}} \log{\left(3 \right)}^{2} + 2 \cdot 3^{x^{2}} x^{2} e^{3^{x^{2}}} \log{\left(3 \right)}^{2} + 3^{x^{2}} e^{3^{x^{2}}} \log{\left(3 \right)} - \frac{4 x}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + 49 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot{\left(7 x \right)}\right)$$
Tercera derivada [src]
  /                                                                                                             / / 2\\                       / / 2\\                      / / 2\\                      / / 2\\                        / / 2\\\
  |                     2                                                           2          / 2\             | \x /|         2             | \x /|        / 2\          | \x /|           2          | \x /|          2             | \x /||
  |      /       2     \          4                2      /       2     \       48*x           \x /  3    3     \3    /      3*x   3    3     \3    /        \x /    2     \3    /        2*x     2     \3    /       2*x   3    3     \3    /|
2*|- 343*\1 + cot (7*x)/  - ------------- - 686*cot (7*x)*\1 + cot (7*x)/ - ------------- + 4*3    *x *log (3)*e        + 4*3    *x *log (3)*e        + 6*x*3    *log (3)*e        + 6*x*3    *log (3)*e        + 12*3    *x *log (3)*e       |
  |                                   3/2                                             5/2                                                                                                                                                     |
  |                         /       2\                                      /       2\                                                                                                                                                        |
  \                         \1 - 4*x /                                      \1 - 4*x /                                                                                                                                                        /
$$2 \left(4 \cdot 3^{3 x^{2}} x^{3} e^{3^{x^{2}}} \log{\left(3 \right)}^{3} + 12 \cdot 3^{2 x^{2}} x^{3} e^{3^{x^{2}}} \log{\left(3 \right)}^{3} + 6 \cdot 3^{2 x^{2}} x e^{3^{x^{2}}} \log{\left(3 \right)}^{2} + 4 \cdot 3^{x^{2}} x^{3} e^{3^{x^{2}}} \log{\left(3 \right)}^{3} + 6 \cdot 3^{x^{2}} x e^{3^{x^{2}}} \log{\left(3 \right)}^{2} - \frac{48 x^{2}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} - 343 \left(\cot^{2}{\left(7 x \right)} + 1\right)^{2} - 686 \left(\cot^{2}{\left(7 x \right)} + 1\right) \cot^{2}{\left(7 x \right)} - \frac{4}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$