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y=sqrt(1-3*x-2*x^2)+3/(2*sqrt2)*arcsin(4x+3/sqrt17)

Derivada de y=sqrt(1-3*x-2*x^2)+3/(2*sqrt2)*arcsin(4x+3/sqrt17)

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

Gráfico:

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Solución

Ha introducido [src]
   ________________                             
  /              2       3        /        3   \
\/  1 - 3*x - 2*x   + -------*asin|4*x + ------|
                          ___     |        ____|
                      2*\/ 2      \      \/ 17 /
$$\sqrt{- 2 x^{2} + \left(1 - 3 x\right)} + \frac{3}{2 \sqrt{2}} \operatorname{asin}{\left(4 x + \frac{3}{\sqrt{17}} \right)}$$
sqrt(1 - 3*x - 2*x^2) + (3/((2*sqrt(2))))*asin(4*x + 3/sqrt(17))
Gráfica
Primera derivada [src]
                                     ___         
                                   \/ 2          
                                12*-----         
     -3/2 - 2*x                      4           
------------------- + ---------------------------
   ________________         _____________________
  /              2         /                   2 
\/  1 - 3*x - 2*x         /      /        3   \  
                         /   1 - |4*x + ------|  
                        /        |        ____|  
                      \/         \      \/ 17 /  
$$\frac{- 2 x - \frac{3}{2}}{\sqrt{- 2 x^{2} + \left(1 - 3 x\right)}} + \frac{12 \frac{\sqrt{2}}{4}}{\sqrt{1 - \left(4 x + \frac{3}{\sqrt{17}}\right)^{2}}}$$
Segunda derivada [src]
                                       2               ___ /    ____       \  
           2                  (3 + 4*x)           12*\/ 2 *\3*\/ 17  + 68*x/  
- ------------------- - --------------------- + ------------------------------
     ________________                     3/2                              3/2
    /              2      /             2\         /                     2\   
  \/  1 - 3*x - 2*x     4*\1 - 3*x - 2*x /         |    /    ____       \ |   
                                                   |    \3*\/ 17  + 68*x/ |   
                                                17*|1 - ------------------|   
                                                   \           289        /   
$$- \frac{\left(4 x + 3\right)^{2}}{4 \left(- 2 x^{2} - 3 x + 1\right)^{\frac{3}{2}}} - \frac{2}{\sqrt{- 2 x^{2} - 3 x + 1}} + \frac{12 \sqrt{2} \left(68 x + 3 \sqrt{17}\right)}{17 \left(1 - \frac{\left(68 x + 3 \sqrt{17}\right)^{2}}{289}\right)^{\frac{3}{2}}}$$
Tercera derivada [src]
  /                                                                                                          2  \
  |                                       ___                           3               ___ /    ____       \   |
  |        3 + 4*x                   16*\/ 2                   (3 + 4*x)           48*\/ 2 *\3*\/ 17  + 68*x/   |
3*|- ------------------- + --------------------------- - --------------------- + -------------------------------|
  |                  3/2                           3/2                     5/2                               5/2|
  |  /             2\      /                     2\        /             2\          /                     2\   |
  |  \1 - 3*x - 2*x /      |    /    ____       \ |      8*\1 - 3*x - 2*x /          |    /    ____       \ |   |
  |                        |    \3*\/ 17  + 68*x/ |                                  |    \3*\/ 17  + 68*x/ |   |
  |                        |1 - ------------------|                              289*|1 - ------------------|   |
  \                        \           289        /                                  \           289        /   /
$$3 \left(- \frac{\left(4 x + 3\right)^{3}}{8 \left(- 2 x^{2} - 3 x + 1\right)^{\frac{5}{2}}} - \frac{4 x + 3}{\left(- 2 x^{2} - 3 x + 1\right)^{\frac{3}{2}}} + \frac{16 \sqrt{2}}{\left(1 - \frac{\left(68 x + 3 \sqrt{17}\right)^{2}}{289}\right)^{\frac{3}{2}}} + \frac{48 \sqrt{2} \left(68 x + 3 \sqrt{17}\right)^{2}}{289 \left(1 - \frac{\left(68 x + 3 \sqrt{17}\right)^{2}}{289}\right)^{\frac{5}{2}}}\right)$$
Gráfico
Derivada de y=sqrt(1-3*x-2*x^2)+3/(2*sqrt2)*arcsin(4x+3/sqrt17)