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пarcsinx/arccosx
Derivada de la función/ arccos/ arcsin/ пarcsinx/arccosx

Derivada de пarcsinx/arccosx

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

Gráfico:

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Solución

Ha introducido [src] 
pi*asin(x)
----------
 acos(x)
πasin⁡(x)acos⁡(x)\frac{\pi \operatorname{asin}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} 
(pi*asin(x))/acos(x)
Gráfica
02468-8-6-4-2-1010-50100
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
         pi                pi*asin(x)     
------------------- + --------------------
   ________              ________         
  /      2              /      2      2   
\/  1 - x  *acos(x)   \/  1 - x  *acos (x)
π1−x2acos⁡(x)+πasin⁡(x)1−x2acos⁡2(x)\frac{\pi}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} + \frac{\pi \operatorname{asin}{\left(x \right)}}{\sqrt{1 - x^{2}} \operatorname{acos}^{2}{\left(x \right)}}
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Segunda derivada [src] 
   /                                  /     x                2        \        \
   |                                  |----------- - -----------------|*asin(x)|
   |                                  |        3/2   /      2\        |        |
   |                                  |/     2\      \-1 + x /*acos(x)|        |
   |     x                2           \\1 - x /                       /        |
pi*|----------- - ----------------- + -----------------------------------------|
   |        3/2   /      2\                            acos(x)                 |
   |/     2\      \-1 + x /*acos(x)                                            |
   \\1 - x /                                                                   /
--------------------------------------------------------------------------------
                                    acos(x)
π(x(1−x2)32+(x(1−x2)32−2(x2−1)acos⁡(x))asin⁡(x)acos⁡(x)−2(x2−1)acos⁡(x))acos⁡(x)\frac{\pi \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{\left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}}\right) \operatorname{asin}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}}\right)}{\operatorname{acos}{\left(x \right)}}
Simplificar
Tercera derivada [src] 
   /                 /                     2                                               \                                                                   \
   |            2    |     1            3*x                6                    6*x        |                                  /     x                2        \|
   |         3*x     |----------- + ----------- + -------------------- + ------------------|*asin(x)                        3*|----------- - -----------------||
   |  -1 + -------   |        3/2           5/2           3/2                     2        |                                  |        3/2   /      2\        ||
   |             2   |/     2\      /     2\      /     2\        2      /      2\         |                                  |/     2\      \-1 + x /*acos(x)||
   |       -1 + x    \\1 - x /      \1 - x /      \1 - x /   *acos (x)   \-1 + x / *acos(x)/                  3*x             \\1 - x /                       /|
pi*|- ------------ + ------------------------------------------------------------------------------- + ------------------ + -----------------------------------|
   |          3/2                                        acos(x)                                                2                      ________                |
   |  /     2\                                                                                         /      2\                      /      2                 |
   \  \1 - x /                                                                                         \-1 + x / *acos(x)           \/  1 - x  *acos(x)        /
----------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                            acos(x)
π(3x(x2−1)2acos⁡(x)+(3x2(1−x2)52+6x(x2−1)2acos⁡(x)+1(1−x2)32+6(1−x2)32acos⁡2(x))asin⁡(x)acos⁡(x)+3(x(1−x2)32−2(x2−1)acos⁡(x))1−x2acos⁡(x)−3x2x2−1−1(1−x2)32)acos⁡(x)\frac{\pi \left(\frac{3 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}{\left(x \right)}} + \frac{\left(\frac{3 x^{2}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{6 x}{\left(x^{2} - 1\right)^{2} \operatorname{acos}{\left(x \right)}} + \frac{1}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{6}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \right)}}\right) \operatorname{asin}{\left(x \right)}}{\operatorname{acos}{\left(x \right)}} + \frac{3 \left(\frac{x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{2}{\left(x^{2} - 1\right) \operatorname{acos}{\left(x \right)}}\right)}{\sqrt{1 - x^{2}} \operatorname{acos}{\left(x \right)}} - \frac{\frac{3 x^{2}}{x^{2} - 1} - 1}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)}{\operatorname{acos}{\left(x \right)}}
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Gráfico
Derivada de пarcsinx/arccosx
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