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y=log((x^2)(arcsin^2)-3x)
Derivada de la función/ y=log/ (x^2)/ sin^2/ arcsin/ y=log((x^2)(arcsin^2)-3x)

Derivada de y=log((x^2)(arcsin^2)-3x)

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

Gráfico:

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Solución

Ha introducido [src] 
   / 2     2         \
log\x *asin (x) - 3*x/
log⁡(x2asin⁡2(x)−3x)\log{\left(x^{2} \operatorname{asin}^{2}{\left(x \right)} - 3 x \right)} 
log(x^2*asin(x)^2 - 3*x)
Gráfica
02468-8-6-4-2-1010-2020
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Trazar el gráfico f'(x)
Primera derivada [src] 
                       2        
             2      2*x *asin(x)
-3 + 2*x*asin (x) + ------------
                       ________ 
                      /      2  
                    \/  1 - x   
--------------------------------
        2     2                 
       x *asin (x) - 3*x
2x2asin⁡(x)1−x2+2xasin⁡2(x)−3x2asin⁡2(x)−3x\frac{\frac{2 x^{2} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 2 x \operatorname{asin}^{2}{\left(x \right)} - 3}{x^{2} \operatorname{asin}^{2}{\left(x \right)} - 3 x}
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Segunda derivada [src] 
                                                         2                             
                       /                       2        \                              
                       |             2      2*x *asin(x)|                              
                       |-3 + 2*x*asin (x) + ------------|                              
                       |                       ________ |                              
                  2    |                      /      2  |       3                      
      2        2*x     \                    \/  1 - x   /    2*x *asin(x)   8*x*asin(x)
2*asin (x) - ------- - ----------------------------------- + ------------ + -----------
                   2             /           2   \                   3/2       ________
             -1 + x            x*\-3 + x*asin (x)/           /     2\         /      2 
                                                             \1 - x /       \/  1 - x  
---------------------------------------------------------------------------------------
                                    /           2   \                                  
                                  x*\-3 + x*asin (x)/
2x3asin⁡(x)(1−x2)32−2x2x2−1+8xasin⁡(x)1−x2+2asin⁡2(x)−(2x2asin⁡(x)1−x2+2xasin⁡2(x)−3)2x(xasin⁡2(x)−3)x(xasin⁡2(x)−3)\frac{\frac{2 x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2 x^{2}}{x^{2} - 1} + \frac{8 x \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 2 \operatorname{asin}^{2}{\left(x \right)} - \frac{\left(\frac{2 x^{2} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 2 x \operatorname{asin}^{2}{\left(x \right)} - 3\right)^{2}}{x \left(x \operatorname{asin}^{2}{\left(x \right)} - 3\right)}}{x \left(x \operatorname{asin}^{2}{\left(x \right)} - 3\right)}
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Tercera derivada [src] 
  /                                                                         3                                                                                                                      \
  |                                       /                       2        \                                    /                       2        \ /               2       3                      \|
  |                                       |             2      2*x *asin(x)|                                    |             2      2*x *asin(x)| |    2         x       x *asin(x)   4*x*asin(x)||
  |                                       |-3 + 2*x*asin (x) + ------------|                                  3*|-3 + 2*x*asin (x) + ------------|*|asin (x) - ------- + ----------- + -----------||
  |                                       |                       ________ |                                    |                       ________ | |                 2           3/2      ________||
  |                  3                    |                      /      2  |       4              2             |                      /      2  | |           -1 + x    /     2\        /      2 ||
  |    6*x        3*x        6*asin(x)    \                    \/  1 - x   /    3*x *asin(x)   7*x *asin(x)     \                    \/  1 - x   / \                     \1 - x /      \/  1 - x  /|
2*|- ------- + ---------- + ----------- + ----------------------------------- + ------------ + ------------ - -------------------------------------------------------------------------------------|
  |        2            2      ________                              2                  5/2            3/2                                       /           2   \                                 |
  |  -1 + x    /      2\      /      2            2 /           2   \           /     2\       /     2\                                        x*\-3 + x*asin (x)/                                 |
  \            \-1 + x /    \/  1 - x            x *\-3 + x*asin (x)/           \1 - x /       \1 - x /                                                                                            /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                          /           2   \                                                                                         
                                                                                        x*\-3 + x*asin (x)/
2(3x4asin⁡(x)(1−x2)52+3x3(x2−1)2+7x2asin⁡(x)(1−x2)32−6xx2−1+6asin⁡(x)1−x2−3(2x2asin⁡(x)1−x2+2xasin⁡2(x)−3)(x3asin⁡(x)(1−x2)32−x2x2−1+4xasin⁡(x)1−x2+asin⁡2(x))x(xasin⁡2(x)−3)+(2x2asin⁡(x)1−x2+2xasin⁡2(x)−3)3x2(xasin⁡2(x)−3)2)x(xasin⁡2(x)−3)\frac{2 \left(\frac{3 x^{4} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x^{3}}{\left(x^{2} - 1\right)^{2}} + \frac{7 x^{2} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6 x}{x^{2} - 1} + \frac{6 \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} - \frac{3 \left(\frac{2 x^{2} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 2 x \operatorname{asin}^{2}{\left(x \right)} - 3\right) \left(\frac{x^{3} \operatorname{asin}{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{x^{2}}{x^{2} - 1} + \frac{4 x \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + \operatorname{asin}^{2}{\left(x \right)}\right)}{x \left(x \operatorname{asin}^{2}{\left(x \right)} - 3\right)} + \frac{\left(\frac{2 x^{2} \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}}} + 2 x \operatorname{asin}^{2}{\left(x \right)} - 3\right)^{3}}{x^{2} \left(x \operatorname{asin}^{2}{\left(x \right)} - 3\right)^{2}}\right)}{x \left(x \operatorname{asin}^{2}{\left(x \right)} - 3\right)}
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Gráfico
Derivada de y=log((x^2)(arcsin^2)-3x)
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