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y=sqrt(x)*arccos(x)*sqrt(x)-sqrt(1-x)
Derivada de la función/ y=sqrt(x)*arccos(x)*sqrt(x)-sqrt(1-x)

Derivada de y=sqrt(x)*arccos(x)*sqrt(x)-sqrt(1-x)

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

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Solución

Ha introducido [src] 
  ___           ___     _______
\/ x *acos(x)*\/ x  - \/ 1 - x
xxacos⁡(x)−1−x\sqrt{x} \sqrt{x} \operatorname{acos}{\left(x \right)} - \sqrt{1 - x} 
(sqrt(x)*acos(x))*sqrt(x) - sqrt(1 - x)
Gráfica
02468-8-6-4-2-1010-1010
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Primera derivada [src] 
                              /               ___   \
     1        acos(x)     ___ |acos(x)      \/ x    |
----------- + ------- + \/ x *|------- - -----------|
    _______      2            |    ___      ________|
2*\/ 1 - x                    |2*\/ x      /      2 |
                              \          \/  1 - x  /
x(−x1−x2+acos⁡(x)2x)+acos⁡(x)2+121−x\sqrt{x} \left(- \frac{\sqrt{x}}{\sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{2 \sqrt{x}}\right) + \frac{\operatorname{acos}{\left(x \right)}}{2} + \frac{1}{2 \sqrt{1 - x}}
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Segunda derivada [src] 
                                                                                                 ___  
                                                                                 acos(x)     2*\/ x   
                                                                               - ------- + -----------
                                                                                    ___       ________
                                 /                                    3/2  \      \/ x       /      2 
    1             2          ___ |acos(x)           4              4*x     |               \/  1 - x  
---------- - ----------- - \/ x *|------- + ----------------- + -----------| - -----------------------
       3/2      ________         |   3/2             ________           3/2|              ___         
(1 - x)        /      2          |  x         ___   /      2    /     2\   |            \/ x          
             \/  1 - x           \          \/ x *\/  1 - x     \1 - x /   /                          
------------------------------------------------------------------------------------------------------
                                                  4
−x(4x32(1−x2)32+4x1−x2+acos⁡(x)x32)−21−x2+1(1−x)32−2x1−x2−acos⁡(x)xx4\frac{- \sqrt{x} \left(\frac{4 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4}{\sqrt{x} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{\frac{3}{2}}}\right) - \frac{2}{\sqrt{1 - x^{2}}} + \frac{1}{\left(1 - x\right)^{\frac{3}{2}}} - \frac{\frac{2 \sqrt{x}}{\sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{\sqrt{x}}}{\sqrt{x}}}{4}
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Tercera derivada [src] 
                               ___                                                                                          /                                    3/2  \
               acos(x)     2*\/ x                                                                                           |acos(x)           4              4*x     |
             - ------- + -----------                                                                                      2*|------- + ----------------- + -----------|
                  ___       ________                                                                                        |   3/2             ________           3/2|
                \/ x       /      2          /                                        ___          5/2  \                   |  x         ___   /      2    /     2\   |
    3                    \/  1 - x       ___ |         6           3*acos(x)     20*\/ x       24*x     |       4*x         \          \/ x *\/  1 - x     \1 - x /   /
---------- + ----------------------- - \/ x *|- ---------------- - --------- + ----------- + -----------| - ----------- - ---------------------------------------------
       5/2              3/2                  |          ________       5/2             3/2           5/2|           3/2                         ___                    
(1 - x)                x                     |   3/2   /      2       x        /     2\      /     2\   |   /     2\                          \/ x                     
                                             \  x   *\/  1 - x                 \1 - x /      \1 - x /   /   \1 - x /                                                   
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                   8
−x(24x52(1−x2)52+20x(1−x2)32−6x321−x2−3acos⁡(x)x52)−4x(1−x2)32+3(1−x)52−2(4x32(1−x2)32+4x1−x2+acos⁡(x)x32)x+2x1−x2−acos⁡(x)xx328\frac{- \sqrt{x} \left(\frac{24 x^{\frac{5}{2}}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{20 \sqrt{x}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{6}{x^{\frac{3}{2}} \sqrt{1 - x^{2}}} - \frac{3 \operatorname{acos}{\left(x \right)}}{x^{\frac{5}{2}}}\right) - \frac{4 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x\right)^{\frac{5}{2}}} - \frac{2 \left(\frac{4 x^{\frac{3}{2}}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{4}{\sqrt{x} \sqrt{1 - x^{2}}} + \frac{\operatorname{acos}{\left(x \right)}}{x^{\frac{3}{2}}}\right)}{\sqrt{x}} + \frac{\frac{2 \sqrt{x}}{\sqrt{1 - x^{2}}} - \frac{\operatorname{acos}{\left(x \right)}}{\sqrt{x}}}{x^{\frac{3}{2}}}}{8}
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Gráfico
Derivada de y=sqrt(x)*arccos(x)*sqrt(x)-sqrt(1-x)
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