Sr Examen

Otras calculadoras


y=arcsin^3(2x)/√1-4x^2

Derivada de y=arcsin^3(2x)/√1-4x^2

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
    3            
asin (2*x)      2
---------- - 4*x 
    ___          
  \/ 1           
$$- 4 x^{2} + \frac{\operatorname{asin}^{3}{\left(2 x \right)}}{\sqrt{1}}$$
asin(2*x)^3/sqrt(1) - 4*x^2
Gráfica
Primera derivada [src]
              2     
        6*asin (2*x)
-8*x + -------------
          __________
         /        2 
       \/  1 - 4*x  
$$- 8 x + \frac{6 \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$
Segunda derivada [src]
  /                           2     \
  |     3*asin(2*x)   3*x*asin (2*x)|
8*|-1 - ----------- + --------------|
  |              2              3/2 |
  |      -1 + 4*x     /       2\    |
  \                   \1 - 4*x /    /
$$8 \left(\frac{3 x \operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - 1 - \frac{3 \operatorname{asin}{\left(2 x \right)}}{4 x^{2} - 1}\right)$$
Tercera derivada [src]
   /                      2                              2     2     \
   |      2           asin (2*x)    12*x*asin(2*x)   12*x *asin (2*x)|
24*|------------- + ------------- + -------------- + ----------------|
   |          3/2             3/2               2               5/2  |
   |/       2\      /       2\       /        2\      /       2\     |
   \\1 - 4*x /      \1 - 4*x /       \-1 + 4*x /      \1 - 4*x /     /
$$24 \left(\frac{12 x^{2} \operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left(2 x \right)}}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$
Gráfico
Derivada de y=arcsin^3(2x)/√1-4x^2