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y=arccos(((1-sqrt(x))/(1+sqrt(x)))^2)

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  • Derivada de:
  • Derivada de x^-4/5 Derivada de x^-4/5
  • Derivada de x^2*5^x Derivada de x^2*5^x
  • Derivada de x/(1+e^x) Derivada de x/(1+e^x)
  • Derivada de u/v

  • Expresiones idénticas

  • y=arccos(((uno -sqrt(x))/(uno +sqrt(x)))^ dos)
  • y es igual a arc coseno de (((1 menos raíz cuadrada de (x)) dividir por (1 más raíz cuadrada de (x))) al cuadrado )
  • y es igual a arc coseno de (((uno menos raíz cuadrada de (x)) dividir por (uno más raíz cuadrada de (x))) en el grado dos)
  • y=arccos(((1-√(x))/(1+√(x)))^2)
  • y=arccos(((1-sqrt(x))/(1+sqrt(x)))2)
  • y=arccos1-sqrtx/1+sqrtx2
  • y=arccos(((1-sqrt(x))/(1+sqrt(x)))²)
  • y=arccos(((1-sqrt(x))/(1+sqrt(x))) en el grado 2)
  • y=arccos1-sqrtx/1+sqrtx^2
  • y=arccos(((1-sqrt(x)) dividir por (1+sqrt(x)))^2)

  • Expresiones semejantes

  • y=arccos(((1-sqrt(x))/(1-sqrt(x)))^2)
  • y=arccos(((1+sqrt(x))/(1+sqrt(x)))^2)
Derivada de la función/ y=arccos(((1-sqrt(x))/(1+sqrt(x)))^2)

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
    /           2\
    |/      ___\ |
    ||1 - \/ x | |
acos||---------| |
    ||      ___| |
    \\1 + \/ x / /
acos⁡((1−xx+1)2)\operatorname{acos}{\left(\left(\frac{1 - \sqrt{x}}{\sqrt{x} + 1}\right)^{2} \right)} 
acos(((1 - sqrt(x))/(1 + sqrt(x)))^2)
Gráfica
02468-8-6-4-2-10102-2
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
             /                                ___     \ 
 /      ___\ |          1               1 - \/ x      | 
-\1 - \/ x /*|- ----------------- - ------------------| 
             |    ___ /      ___\                    2| 
             |  \/ x *\1 + \/ x /     ___ /      ___\ | 
             \                      \/ x *\1 + \/ x / / 
--------------------------------------------------------
                             __________________         
                            /                4          
                           /      /      ___\           
         /      ___\      /       \1 - \/ x /           
         \1 + \/ x /*    /    1 - ------------          
                        /                    4          
                       /          /      ___\           
                     \/           \1 + \/ x /
−(1−x)(−1−xx(x+1)2−1x(x+1))(x+1)−(1−x)4(x+1)4+1- \frac{\left(1 - \sqrt{x}\right) \left(- \frac{1 - \sqrt{x}}{\sqrt{x} \left(\sqrt{x} + 1\right)^{2}} - \frac{1}{\sqrt{x} \left(\sqrt{x} + 1\right)}\right)}{\left(\sqrt{x} + 1\right) \sqrt{- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1}}
Simplificar
Segunda derivada [src] 
                               /                                   ___        /       ___\\                                                                    2
            ___   /       ___\ |   1           2            -1 + \/ x       2*\-1 + \/ x /|                /            ___\                4 /            ___\ 
     -1 + \/ x    \-1 + \/ x /*|- ---- - ------------- + ---------------- + --------------|   /       ___\ |     -1 + \/ x |    /       ___\  |     -1 + \/ x | 
-1 + ----------                |   3/2     /      ___\    3/2 /      ___\                2|   \-1 + \/ x /*|-1 + ----------|    \-1 + \/ x / *|-1 + ----------| 
           ___                 |  x      x*\1 + \/ x /   x   *\1 + \/ x /     /      ___\ |                |           ___ |                  |           ___ | 
     1 + \/ x                  \                                            x*\1 + \/ x / /                \     1 + \/ x  /                  \     1 + \/ x  / 
--------------- - ------------------------------------------------------------------------- - ------------------------------ - ---------------------------------
      2*x                                             2                                                  /      ___\                          /               4\
                                                                                                     2*x*\1 + \/ x /                        4 |    /      ___\ |
                                                                                                                                 /      ___\  |    \1 - \/ x / |
                                                                                                                               x*\1 + \/ x / *|1 - ------------|
                                                                                                                                              |               4|
                                                                                                                                              |    /      ___\ |
                                                                                                                                              \    \1 + \/ x / /
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                                                            /      ___\       /       \1 - \/ x /                                                               
                                                            \1 + \/ x / *    /    1 - ------------                                                              
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                                                                         \/           \1 + \/ x /
−(x−1)(2(x−1)x(x+1)2−2x(x+1)+x−1x32(x+1)−1x32)2−(x−1)4(x−1x+1−1)2x(x+1)4(−(1−x)4(x+1)4+1)−(x−1)(x−1x+1−1)2x(x+1)+x−1x+1−12x(x+1)2−(1−x)4(x+1)4+1\frac{- \frac{\left(\sqrt{x} - 1\right) \left(\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right)}{2} - \frac{\left(\sqrt{x} - 1\right)^{4} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2}}{x \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} - \frac{\left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)}{2 x \left(\sqrt{x} + 1\right)} + \frac{\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1}{2 x}}{\left(\sqrt{x} + 1\right)^{2} \sqrt{- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1}}
Simplificar
Tercera derivada [src] 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 /                              2                                    2\
                                     ___        /       ___\                                    /                                                        ___         /       ___\       /       ___\ \                                                                      /                                   ___        /       ___\\                                                                     2                                      2                                        3                4 /            ___\ /                                   ___        /       ___\\               3 /            ___\ |           ___    /       ___\        /       ___\     /       ___\ |
     1           2            -1 + \/ x       2*\-1 + \/ x /               ___     /       ___\ |   1           2                  2              -1 + \/ x        2*\-1 + \/ x /     2*\-1 + \/ x / |                ___                  /            ___\   /       ___\ |   1           2            -1 + \/ x       2*\-1 + \/ x /|                /            ___\                 4 /            ___\                    3 /            ___\                      7 /            ___\     /       ___\  |     -1 + \/ x | |   1           2            -1 + \/ x       2*\-1 + \/ x /|   /       ___\  |     -1 + \/ x | |3   -1 + \/ x     \-1 + \/ x /      8*\-1 + \/ x /   5*\-1 + \/ x / |
  - ---- - ------------- + ---------------- + --------------        -1 + \/ x    3*\-1 + \/ x /*|- ---- - -------------- - ----------------- + ---------------- + --------------- + -----------------|         -1 + \/ x      /       ___\ |     -1 + \/ x |   \-1 + \/ x /*|- ---- - ------------- + ---------------- + --------------|   /       ___\ |     -1 + \/ x |     /       ___\  |     -1 + \/ x |        /       ___\  |     -1 + \/ x |          /       ___\  |     -1 + \/ x |     \-1 + \/ x / *|-1 + ----------|*|- ---- - ------------- + ---------------- + --------------|   \-1 + \/ x / *|-1 + ----------|*|- - ---------- + ---------------- - -------------- + ---------------|
     3/2     /      ___\    3/2 /      ___\                2   -1 + ----------                  |   5/2    2 /      ___\                   2    5/2 /      ___\                 2                   3|    -1 + ----------     \-1 + \/ x /*|-1 + ----------|                |   3/2     /      ___\    3/2 /      ___\                2|   \-1 + \/ x /*|-1 + ----------|     \-1 + \/ x / *|-1 + ----------|        \-1 + \/ x / *|-1 + ----------|        3*\-1 + \/ x / *|-1 + ----------|                   |           ___ | |   3/2     /      ___\    3/2 /      ___\                2|                 |           ___ | |x       3/2       3/2 /      ___\     /      ___\                  2|
    x      x*\1 + \/ x /   x   *\1 + \/ x /     /      ___\               ___                   |  x      x *\1 + \/ x /    3/2 /      ___\    x   *\1 + \/ x /    2 /      ___\     3/2 /      ___\ |               ___                   |           ___ |                |  x      x*\1 + \/ x /   x   *\1 + \/ x /     /      ___\ |                |           ___ |                   |           ___ |                      |           ___ |                        |           ___ |                   \     1 + \/ x  / |  x      x*\1 + \/ x /   x   *\1 + \/ x /     /      ___\ |                 \     1 + \/ x  / |       x         x   *\1 + \/ x /   x*\1 + \/ x /       /      ___\ |
                                              x*\1 + \/ x /         1 + \/ x                    \                          x   *\1 + \/ x /                       x *\1 + \/ x /    x   *\1 + \/ x / /         1 + \/ x                    \     1 + \/ x  /                \                                            x*\1 + \/ x / /                \     1 + \/ x  /                   \     1 + \/ x  /                      \     1 + \/ x  /                        \     1 + \/ x  /                                     \                                            x*\1 + \/ x / /                                   \                                                      x*\1 + \/ x / /
- ---------------------------------------------------------- - --------------- + --------------------------------------------------------------------------------------------------------------------- - ------------------ + ------------------------------ + ------------------------------------------------------------------------- + ------------------------------ + ------------------------------------ - ------------------------------------ + ------------------------------------- + -------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------
                               ___                                      2                                                                  4                                                                3/2 /      ___\                          2                                        ___ /      ___\                                        2 /      ___\                            /               4\                     /               4\                                       2                                                 /               4\                                                                                   /               4\                                
                           2*\/ x                                    4*x                                                                                                                                 2*x   *\1 + \/ x /           3/2 /      ___\                                     2*\/ x *\1 + \/ x /                                     4*x *\1 + \/ x /                          5 |    /      ___\ |                   4 |    /      ___\ |                     /               4\                                                4 |    /      ___\ |                                                                                 4 |    /      ___\ |                                
                                                                                                                                                                                                                                   2*x   *\1 + \/ x /                                                                                                                        3/2 /      ___\  |    \1 - \/ x / |    3/2 /      ___\  |    \1 - \/ x / |                   8 |    /      ___\ |                                 ___ /      ___\  |    \1 - \/ x / |                                                                  ___ /      ___\  |    \1 - \/ x / |                                
                                                                                                                                                                                                                                                                                                                                                                            x   *\1 + \/ x / *|1 - ------------|   x   *\1 + \/ x / *|1 - ------------|    3/2 /      ___\  |    \1 - \/ x / |                               \/ x *\1 + \/ x / *|1 - ------------|                                                              2*\/ x *\1 + \/ x / *|1 - ------------|                                
                                                                                                                                                                                                                                                                                                                                                                                              |               4|                     |               4|   x   *\1 + \/ x / *|1 - ------------|                                                  |               4|                                                                                   |               4|                                
                                                                                                                                                                                                                                                                                                                                                                                              |    /      ___\ |                     |    /      ___\ |                     |               4|                                                  |    /      ___\ |                                                                                   |    /      ___\ |                                
                                                                                                                                                                                                                                                                                                                                                                                              \    \1 + \/ x / /                     \    \1 + \/ x / /                     |    /      ___\ |                                                  \    \1 + \/ x / /                                                                                   \    \1 + \/ x / /                                
                                                                                                                                                                                                                                                                                                                                                                                                                                                                            \    \1 + \/ x / /                                                                                                                                                                                                         
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                                                                                                                                                                                                                                                                                                                                /      ___\       /       \1 - \/ x /                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                \1 + \/ x / *    /    1 - ------------                                                                                                                                                                                                                                                                                                                                 
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                                                                                                                                                                                                                                                                                                                                               /          /      ___\                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                             \/           \1 + \/ x /
3(x−1)(2(x−1)x2(x+1)2−2x2(x+1)+2(x−1)x32(x+1)3−2x32(x+1)2+x−1x52(x+1)−1x52)4+(x−1)(x−1x+1−1)4x2(x+1)−x−1x+1−14x2+(x−1)4(x−1x+1−1)(2(x−1)x(x+1)2−2x(x+1)+x−1x32(x+1)−1x32)x(x+1)4(−(1−x)4(x+1)4+1)+(x−1)3(x−1x+1−1)(5(x−1)2x(x+1)2−8(x−1)x(x+1)+3x+(x−1)2x32(x+1)−x−1x32)2x(x+1)4(−(1−x)4(x+1)4+1)+(x−1)(2(x−1)x(x+1)2−2x(x+1)+x−1x32(x+1)−1x32)2x(x+1)−2(x−1)x(x+1)2−2x(x+1)+x−1x32(x+1)−1x322x+3(x−1)7(x−1x+1−1)3x32(x+1)8(−(1−x)4(x+1)4+1)2+(x−1)4(x−1x+1−1)2x32(x+1)5(−(1−x)4(x+1)4+1)−(x−1)3(x−1x+1−1)2x32(x+1)4(−(1−x)4(x+1)4+1)+(x−1)(x−1x+1−1)2x32(x+1)2−x−1x+1−12x32(x+1)(x+1)2−(1−x)4(x+1)4+1\frac{\frac{3 \left(\sqrt{x} - 1\right) \left(\frac{2 \left(\sqrt{x} - 1\right)}{x^{2} \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x^{2} \left(\sqrt{x} + 1\right)} + \frac{2 \left(\sqrt{x} - 1\right)}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{3}} - \frac{2}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} + \frac{\sqrt{x} - 1}{x^{\frac{5}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{5}{2}}}\right)}{4} + \frac{\left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)}{4 x^{2} \left(\sqrt{x} + 1\right)} - \frac{\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1}{4 x^{2}} + \frac{\left(\sqrt{x} - 1\right)^{4} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right) \left(\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right)}{\sqrt{x} \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} + \frac{\left(\sqrt{x} - 1\right)^{3} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right) \left(\frac{5 \left(\sqrt{x} - 1\right)^{2}}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{8 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)} + \frac{3}{x} + \frac{\left(\sqrt{x} - 1\right)^{2}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{\sqrt{x} - 1}{x^{\frac{3}{2}}}\right)}{2 \sqrt{x} \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} + \frac{\left(\sqrt{x} - 1\right) \left(\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}\right)}{2 \sqrt{x} \left(\sqrt{x} + 1\right)} - \frac{\frac{2 \left(\sqrt{x} - 1\right)}{x \left(\sqrt{x} + 1\right)^{2}} - \frac{2}{x \left(\sqrt{x} + 1\right)} + \frac{\sqrt{x} - 1}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)} - \frac{1}{x^{\frac{3}{2}}}}{2 \sqrt{x}} + \frac{3 \left(\sqrt{x} - 1\right)^{7} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{3}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{8} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)^{2}} + \frac{\left(\sqrt{x} - 1\right)^{4} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{5} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} - \frac{\left(\sqrt{x} - 1\right)^{3} \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)^{2}}{x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{4} \left(- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1\right)} + \frac{\left(\sqrt{x} - 1\right) \left(\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1\right)}{2 x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)^{2}} - \frac{\frac{\sqrt{x} - 1}{\sqrt{x} + 1} - 1}{2 x^{\frac{3}{2}} \left(\sqrt{x} + 1\right)}}{\left(\sqrt{x} + 1\right)^{2} \sqrt{- \frac{\left(1 - \sqrt{x}\right)^{4}}{\left(\sqrt{x} + 1\right)^{4}} + 1}}
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Gráfico
Derivada de y=arccos(((1-sqrt(x))/(1+sqrt(x)))^2)
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