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y=x*arcsin√(x/(x+1))-√x+arctg√x
Derivada de la función/ y=x*arcsin√(x/(x+1))-√x+arctg√x

Derivada de y=x*arcsin√(x/(x+1))-√x+arctg√x

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
      /    _______\                      
      |   /   x   |     ___       /  ___\
x*asin|  /  ----- | - \/ x  + atan\\/ x /
      \\/   x + 1 /
(−x+xasin⁡(xx+1))+atan⁡(x)\left(- \sqrt{x} + x \operatorname{asin}{\left(\sqrt{\frac{x}{x + 1}} \right)}\right) + \operatorname{atan}{\left(\sqrt{x} \right)} 
x*asin(sqrt(x/(x + 1))) - sqrt(x) + atan(sqrt(x))
Gráfica
02468-8-6-4-2-1010020
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                  _______                                                     
                                 /   x            /    1           x     \                    
                                /  ----- *(x + 1)*|--------- - ----------|                    
                              \/   x + 1          |2*(x + 1)            2|       /    _______\
     1             1                              \            2*(x + 1) /       |   /   x   |
- ------- + --------------- + -------------------------------------------- + asin|  /  ----- |
      ___       ___                             ___________                      \\/   x + 1 /
  2*\/ x    2*\/ x *(1 + x)                    /       x                                      
                                              /  1 - -----                                    
                                            \/       x + 1
xx+1(x+1)(−x2(x+1)2+12(x+1))−xx+1+1+asin⁡(xx+1)−12x+12x(x+1)\frac{\sqrt{\frac{x}{x + 1}} \left(x + 1\right) \left(- \frac{x}{2 \left(x + 1\right)^{2}} + \frac{1}{2 \left(x + 1\right)}\right)}{\sqrt{- \frac{x}{x + 1} + 1}} + \operatorname{asin}{\left(\sqrt{\frac{x}{x + 1}} \right)} - \frac{1}{2 \sqrt{x}} + \frac{1}{2 \sqrt{x} \left(x + 1\right)}
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Segunda derivada [src] 
                                           _______             2       _______             2         _______                      _______             
                                          /   x    /       x  \       /   x    /       x  \         /   x    /       x  \        /   x    /       x  \
                                         /  ----- *|-1 + -----|      /  ----- *|-1 + -----|    2*  /  ----- *|-1 + -----|   2*  /  ----- *|-1 + -----|
 1          1               2          \/   1 + x  \     1 + x/    \/   1 + x  \     1 + x/      \/   1 + x  \     1 + x/     \/   1 + x  \     1 + x/
---- - ------------ - -------------- + ------------------------- + ------------------------- - -------------------------- + --------------------------
 3/2    3/2             ___        2             ___________                            3/2              ___________                     ___________  
x      x   *(1 + x)   \/ x *(1 + x)             /       x                    /      x  \                /       x                       /       x     
                                           x*  /  1 - -----          (1 + x)*|1 - -----|           x*  /  1 - -----          (1 + x)*  /  1 - -----   
                                             \/       1 + x                  \    1 + x/             \/       1 + x                  \/       1 + x   
------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                          4
2xx+1(xx+1−1)(x+1)−xx+1+1+xx+1(xx+1−1)2(x+1)(−xx+1+1)32+xx+1(xx+1−1)2x−xx+1+1−2xx+1(xx+1−1)x−xx+1+1−2x(x+1)2+1x32−1x32(x+1)4\frac{\frac{2 \sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)}{\left(x + 1\right) \sqrt{- \frac{x}{x + 1} + 1}} + \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{2}}{\left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)^{\frac{3}{2}}} + \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{2}}{x \sqrt{- \frac{x}{x + 1} + 1}} - \frac{2 \sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)}{x \sqrt{- \frac{x}{x + 1} + 1}} - \frac{2}{\sqrt{x} \left(x + 1\right)^{2}} + \frac{1}{x^{\frac{3}{2}}} - \frac{1}{x^{\frac{3}{2}} \left(x + 1\right)}}{4}
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Tercera derivada [src] 
                                                                   _______                    _______             2       _______                      _______             3       _______             3         _______                       _______             2       _______             3        _______             2 
                                                                  /   x    /       x  \      /   x    /       x  \       /   x    /       x  \        /   x    /       x  \       /   x    /       x  \         /   x    /       x  \         /   x    /       x  \       /   x    /       x  \        /   x    /       x  \  
                                                                 /  ----- *|-1 + -----|     /  ----- *|-1 + -----|      /  ----- *|-1 + -----|   3*  /  ----- *|-1 + -----|      /  ----- *|-1 + -----|        /  ----- *|-1 + -----|    3*  /  ----- *|-1 + -----|      /  ----- *|-1 + -----|       /  ----- *|-1 + -----|  
    3            1                 1                3          \/   1 + x  \     1 + x/   \/   1 + x  \     1 + x/    \/   1 + x  \     1 + x/     \/   1 + x  \     1 + x/    \/   1 + x  \     1 + x/      \/   1 + x  \     1 + x/      \/   1 + x  \     1 + x/    \/   1 + x  \     1 + x/     \/   1 + x  \     1 + x/  
- ------ + -------------- + --------------- + -------------- + ------------------------ - ------------------------- - ------------------------ - --------------------------- - ------------------------- + --------------------------- - --------------------------- - -------------------------- + --------------------------
     5/2     ___        3      3/2        2      5/2                      ___________                          3/2                 ___________                          5/2                ___________                     ___________                   ___________                          3/2                          3/2
  8*x      \/ x *(1 + x)    2*x   *(1 + x)    8*x   *(1 + x)        2    /       x                2 /      x  \              2    /       x                2 /      x  \             2    /       x                       /       x                     /       x                  /      x  \                  /      x  \   
                                                                 2*x *  /  1 - -----       (1 + x) *|1 - -----|       (1 + x) *  /  1 - -----     8*(1 + x) *|1 - -----|          8*x *  /  1 - -----      2*x*(1 + x)*  /  1 - -----    4*x*(1 + x)*  /  1 - -----    4*x*(1 + x)*|1 - -----|      4*x*(1 + x)*|1 - -----|   
                                                                      \/       1 + x                \    1 + x/                \/       1 + x                \    1 + x/               \/       1 + x                  \/       1 + x                \/       1 + x                \    1 + x/                  \    1 + x/
−xx+1(xx+1−1)(x+1)2−xx+1+1−xx+1(xx+1−1)2(x+1)2(−xx+1+1)32−3xx+1(xx+1−1)38(x+1)2(−xx+1+1)52−3xx+1(xx+1−1)24x(x+1)−xx+1+1+xx+1(xx+1−1)2x(x+1)−xx+1+1−xx+1(xx+1−1)34x(x+1)(−xx+1+1)32+xx+1(xx+1−1)24x(x+1)(−xx+1+1)32−xx+1(xx+1−1)38x2−xx+1+1+xx+1(xx+1−1)2x2−xx+1+1+1x(x+1)3+12x32(x+1)2−38x52+38x52(x+1)- \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)}{\left(x + 1\right)^{2} \sqrt{- \frac{x}{x + 1} + 1}} - \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{2}}{\left(x + 1\right)^{2} \left(- \frac{x}{x + 1} + 1\right)^{\frac{3}{2}}} - \frac{3 \sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{3}}{8 \left(x + 1\right)^{2} \left(- \frac{x}{x + 1} + 1\right)^{\frac{5}{2}}} - \frac{3 \sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{2}}{4 x \left(x + 1\right) \sqrt{- \frac{x}{x + 1} + 1}} + \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)}{2 x \left(x + 1\right) \sqrt{- \frac{x}{x + 1} + 1}} - \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{3}}{4 x \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)^{\frac{3}{2}}} + \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{2}}{4 x \left(x + 1\right) \left(- \frac{x}{x + 1} + 1\right)^{\frac{3}{2}}} - \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)^{3}}{8 x^{2} \sqrt{- \frac{x}{x + 1} + 1}} + \frac{\sqrt{\frac{x}{x + 1}} \left(\frac{x}{x + 1} - 1\right)}{2 x^{2} \sqrt{- \frac{x}{x + 1} + 1}} + \frac{1}{\sqrt{x} \left(x + 1\right)^{3}} + \frac{1}{2 x^{\frac{3}{2}} \left(x + 1\right)^{2}} - \frac{3}{8 x^{\frac{5}{2}}} + \frac{3}{8 x^{\frac{5}{2}} \left(x + 1\right)}
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Gráfico
Derivada de y=x*arcsin√(x/(x+1))-√x+arctg√x
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