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y=3x^2*arcsin(x^2+3)

Derivada de y=3x^2*arcsin(x^2+3)

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

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Solución

Ha introducido [src]
   2     / 2    \
3*x *asin\x  + 3/
$$3 x^{2} \operatorname{asin}{\left(x^{2} + 3 \right)}$$
(3*x^2)*asin(x^2 + 3)
Gráfica
Primera derivada [src]
                              3       
        / 2    \           6*x        
6*x*asin\x  + 3/ + -------------------
                       _______________
                      /             2 
                     /      / 2    \  
                   \/   1 - \x  + 3/  
$$\frac{6 x^{3}}{\sqrt{1 - \left(x^{2} + 3\right)^{2}}} + 6 x \operatorname{asin}{\left(x^{2} + 3 \right)}$$
Segunda derivada [src]
  /                         /        2 /     2\ \               \
  |                       2 |     2*x *\3 + x / |               |
  |                      x *|-1 + --------------|               |
  |                         |                  2|               |
  |           2             |          /     2\ |               |
  |        4*x              \     -1 + \3 + x / /       /     2\|
6*|------------------- - ------------------------ + asin\3 + x /|
  |    _______________         _______________                  |
  |   /             2         /             2                   |
  |  /      /     2\         /      /     2\                    |
  \\/   1 - \3 + x /       \/   1 - \3 + x /                    /
$$6 \left(- \frac{x^{2} \left(\frac{2 x^{2} \left(x^{2} + 3\right)}{\left(x^{2} + 3\right)^{2} - 1} - 1\right)}{\sqrt{1 - \left(x^{2} + 3\right)^{2}}} + \frac{4 x^{2}}{\sqrt{1 - \left(x^{2} + 3\right)^{2}}} + \operatorname{asin}{\left(x^{2} + 3 \right)}\right)$$
Tercera derivada [src]
     /       /                        2\                 \
     |       |              2 /     2\ |                 |
     |     2 |       2   6*x *\3 + x / |                 |
     |    x *|9 + 5*x  - --------------|                 |
     |       |                        2|                 |
     |       |                /     2\ |      2 /     2\ |
     |       \           -1 + \3 + x / /   6*x *\3 + x / |
12*x*|6 + ------------------------------ - --------------|
     |                        2                         2|
     |                /     2\                  /     2\ |
     \            1 - \3 + x /             -1 + \3 + x / /
----------------------------------------------------------
                       _______________                    
                      /             2                     
                     /      /     2\                      
                   \/   1 - \3 + x /                      
$$\frac{12 x \left(- \frac{6 x^{2} \left(x^{2} + 3\right)}{\left(x^{2} + 3\right)^{2} - 1} + \frac{x^{2} \left(- \frac{6 x^{2} \left(x^{2} + 3\right)^{2}}{\left(x^{2} + 3\right)^{2} - 1} + 5 x^{2} + 9\right)}{1 - \left(x^{2} + 3\right)^{2}} + 6\right)}{\sqrt{1 - \left(x^{2} + 3\right)^{2}}}$$
Gráfico
Derivada de y=3x^2*arcsin(x^2+3)