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asin(4*x)/(3*x^2-9*x)
Derivada de la función/ x^2-9/ sin(4*x)/ 3*x^2/ asin(4*x)/(3*x^2-9*x)

Derivada de asin(4*x)/(3*x^2-9*x)

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

Gráfico:

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Solución

Ha introducido [src] 
asin(4*x) 
----------
   2      
3*x  - 9*x
asin⁡(4x)3x2−9x\frac{\operatorname{asin}{\left(4 x \right)}}{3 x^{2} - 9 x} 
asin(4*x)/(3*x^2 - 9*x)
Gráfica
02468-8-6-4-2-10100.5-0.5
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Trazar el gráfico f'(x)
Primera derivada [src] 
             4                (9 - 6*x)*asin(4*x)
--------------------------- + -------------------
   ___________                               2   
  /         2  /   2      \      /   2      \    
\/  1 - 16*x  *\3*x  - 9*x/      \3*x  - 9*x/
(9−6x)asin⁡(4x)(3x2−9x)2+41−16x2(3x2−9x)\frac{\left(9 - 6 x\right) \operatorname{asin}{\left(4 x \right)}}{\left(3 x^{2} - 9 x\right)^{2}} + \frac{4}{\sqrt{1 - 16 x^{2}} \left(3 x^{2} - 9 x\right)}
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Segunda derivada [src] 
  /                 /              2\                                       \
  |                 |    (-3 + 2*x) |                                       |
  |                 |1 - -----------|*asin(4*x)                             |
  |      32         \     x*(-3 + x)/                    4*(-3 + 2*x)       |
2*|-------------- - --------------------------- - --------------------------|
  |           3/2            2                          ___________         |
  |/        2\              x *(-3 + x)            2   /         2          |
  \\1 - 16*x /                                    x *\/  1 - 16*x  *(-3 + x)/
-----------------------------------------------------------------------------
                                  3*(-3 + x)
2(32(1−16x2)32−(1−(2x−3)2x(x−3))asin⁡(4x)x2(x−3)−4(2x−3)x21−16x2(x−3))3(x−3)\frac{2 \left(\frac{32}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{\left(1 - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}\right) \operatorname{asin}{\left(4 x \right)}}{x^{2} \left(x - 3\right)} - \frac{4 \left(2 x - 3\right)}{x^{2} \sqrt{1 - 16 x^{2}} \left(x - 3\right)}\right)}{3 \left(x - 3\right)}
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Tercera derivada [src] 
  /     /           2   \                                                                                               \
  |     |       48*x    |                                  /              2\                 /              2\          |
  |  32*|-1 + ----------|                                  |    (-3 + 2*x) |                 |    (-3 + 2*x) |          |
  |     |              2|                                4*|1 - -----------|      (-3 + 2*x)*|2 - -----------|*asin(4*x)|
  |     \     -1 + 16*x /        32*(-3 + 2*x)             \     x*(-3 + x)/                 \     x*(-3 + x)/          |
2*|- -------------------- - ----------------------- - ------------------------- + --------------------------------------|
  |                 3/2                3/2                 ___________                          2         2             |
  |      /        2\        /        2\                   /         2                          x *(-3 + x)              |
  \    3*\1 - 16*x /        \1 - 16*x /   *(-3 + x)   x*\/  1 - 16*x  *(-3 + x)                                         /
-------------------------------------------------------------------------------------------------------------------------
                                                        x*(-3 + x)
2(−32(48x216x2−1−1)3(1−16x2)32−32(2x−3)(1−16x2)32(x−3)−4(1−(2x−3)2x(x−3))x1−16x2(x−3)+(2−(2x−3)2x(x−3))(2x−3)asin⁡(4x)x2(x−3)2)x(x−3)\frac{2 \left(- \frac{32 \left(\frac{48 x^{2}}{16 x^{2} - 1} - 1\right)}{3 \left(1 - 16 x^{2}\right)^{\frac{3}{2}}} - \frac{32 \left(2 x - 3\right)}{\left(1 - 16 x^{2}\right)^{\frac{3}{2}} \left(x - 3\right)} - \frac{4 \left(1 - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}\right)}{x \sqrt{1 - 16 x^{2}} \left(x - 3\right)} + \frac{\left(2 - \frac{\left(2 x - 3\right)^{2}}{x \left(x - 3\right)}\right) \left(2 x - 3\right) \operatorname{asin}{\left(4 x \right)}}{x^{2} \left(x - 3\right)^{2}}\right)}{x \left(x - 3\right)}
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Gráfico
Derivada de asin(4*x)/(3*x^2-9*x)
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