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y=arcsin(2x)/(sqrt(1-(2x)^2))
Derivada de la función/ y=arcsin(2x)/(sqrt(1-(2x)^2))

Derivada de y=arcsin(2x)/(sqrt(1-(2x)^2))

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

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Solución

Ha introducido [src] 
   asin(2*x)   
---------------
   ____________
  /          2 
\/  1 - (2*x)
asin⁡(2x)1−(2x)2\frac{\operatorname{asin}{\left(2 x \right)}}{\sqrt{1 - \left(2 x\right)^{2}}} 
asin(2*x)/sqrt(1 - (2*x)^2)
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
              2                  4*x*asin(2*x) 
----------------------------- + ---------------
   ____________    __________               3/2
  /          2    /        2    /         2\   
\/  1 - (2*x)  *\/  1 - 4*x     \1 - (2*x) /
4xasin⁡(2x)(1−(2x)2)32+21−4x21−(2x)2\frac{4 x \operatorname{asin}{\left(2 x \right)}}{\left(1 - \left(2 x\right)^{2}\right)^{\frac{3}{2}}} + \frac{2}{\sqrt{1 - 4 x^{2}} \sqrt{1 - \left(2 x\right)^{2}}}
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Segunda derivada [src] 
  /              /           2  \          \
  |              |       12*x   |          |
  |              |-1 + ---------|*asin(2*x)|
  |              |             2|          |
  |    6*x       \     -1 + 4*x /          |
4*|----------- - --------------------------|
  |          2                   3/2       |
  |/       2\          /       2\          |
  \\1 - 4*x /          \1 - 4*x /          /
4(6x(1−4x2)2−(12x24x2−1−1)asin⁡(2x)(1−4x2)32)4 \left(\frac{6 x}{\left(1 - 4 x^{2}\right)^{2}} - \frac{\left(\frac{12 x^{2}}{4 x^{2} - 1} - 1\right) \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)
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Tercera derivada [src] 
  /             2       /           2  \                     /           2  \          \
  |         12*x        |       12*x   |                     |       20*x   |          |
  |  -1 + ---------   3*|-1 + ---------|                 6*x*|-3 + ---------|*asin(2*x)|
  |               2     |             2|          2          |             2|          |
  |       -1 + 4*x      \     -1 + 4*x /      12*x           \     -1 + 4*x /          |
8*|- -------------- - ------------------ + ----------- - ------------------------------|
  |             2                   2                3                     5/2         |
  |   /       2\         /        2\       /       2\            /       2\            |
  \   \1 - 4*x /         \-1 + 4*x /       \1 - 4*x /            \1 - 4*x /            /
8(12x2(1−4x2)3−6x(20x24x2−1−3)asin⁡(2x)(1−4x2)52−3(12x24x2−1−1)(4x2−1)2−12x24x2−1−1(1−4x2)2)8 \left(\frac{12 x^{2}}{\left(1 - 4 x^{2}\right)^{3}} - \frac{6 x \left(\frac{20 x^{2}}{4 x^{2} - 1} - 3\right) \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} - \frac{3 \left(\frac{12 x^{2}}{4 x^{2} - 1} - 1\right)}{\left(4 x^{2} - 1\right)^{2}} - \frac{\frac{12 x^{2}}{4 x^{2} - 1} - 1}{\left(1 - 4 x^{2}\right)^{2}}\right)
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Gráfico
Derivada de y=arcsin(2x)/(sqrt(1-(2x)^2))
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