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

Derivada de y=(√x)arccos(x^2+2x-1)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
  ___     / 2          \
\/ x *acos\x  + 2*x - 1/
xacos⁡((x2+2x)−1)\sqrt{x} \operatorname{acos}{\left(\left(x^{2} + 2 x\right) - 1 \right)} 
sqrt(x)*acos(x^2 + 2*x - 1)
Gráfica
02468-8-6-4-2-1010-2525
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Primera derivada [src] 
    / 2          \          ___               
acos\x  + 2*x - 1/        \/ x *(2 + 2*x)     
------------------ - -------------------------
         ___             _____________________
     2*\/ x             /                   2 
                       /      / 2          \  
                     \/   1 - \x  + 2*x - 1/
−x(2x+2)1−((x2+2x)−1)2+acos⁡((x2+2x)−1)2x- \frac{\sqrt{x} \left(2 x + 2\right)}{\sqrt{1 - \left(\left(x^{2} + 2 x\right) - 1\right)^{2}}} + \frac{\operatorname{acos}{\left(\left(x^{2} + 2 x\right) - 1 \right)}}{2 \sqrt{x}}
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Segunda derivada [src] 
                                                                   /              2 /      2      \\
                                                               ___ |     2*(1 + x) *\-1 + x  + 2*x/|
                                                           2*\/ x *|-1 + --------------------------|
                                                                   |                           2   |
      /      2      \                                              |            /      2      \    |
  acos\-1 + x  + 2*x/              2*(1 + x)                       \       -1 + \-1 + x  + 2*x/    /
- ------------------- - -------------------------------- + -----------------------------------------
            3/2                   ______________________               ______________________       
         4*x                     /                    2               /                    2        
                          ___   /      /      2      \               /      /      2      \         
                        \/ x *\/   1 - \-1 + x  + 2*x/             \/   1 - \-1 + x  + 2*x/
2x(2(x+1)2(x2+2x−1)(x2+2x−1)2−1−1)1−(x2+2x−1)2−2(x+1)x1−(x2+2x−1)2−acos⁡(x2+2x−1)4x32\frac{2 \sqrt{x} \left(\frac{2 \left(x + 1\right)^{2} \left(x^{2} + 2 x - 1\right)}{\left(x^{2} + 2 x - 1\right)^{2} - 1} - 1\right)}{\sqrt{1 - \left(x^{2} + 2 x - 1\right)^{2}}} - \frac{2 \left(x + 1\right)}{\sqrt{x} \sqrt{1 - \left(x^{2} + 2 x - 1\right)^{2}}} - \frac{\operatorname{acos}{\left(x^{2} + 2 x - 1 \right)}}{4 x^{\frac{3}{2}}}
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Tercera derivada [src] 
                                                                                                                  /                                                         2\
                          /              2 /      2      \\                                                       |                                        2 /      2      \ |
                          |     2*(1 + x) *\-1 + x  + 2*x/|                                           ___         |              2      2         6*(1 + x) *\-1 + x  + 2*x/ |
                        3*|-1 + --------------------------|                                       4*\/ x *(1 + x)*|-3 + 2*(1 + x)  + 3*x  + 6*x - ---------------------------|
                          |                           2   |                                                       |                                                      2   |
      /      2      \     |            /      2      \    |                                                       |                                       /      2      \    |
3*acos\-1 + x  + 2*x/     \       -1 + \-1 + x  + 2*x/    /               3*(1 + x)                               \                                  -1 + \-1 + x  + 2*x/    /
--------------------- + ----------------------------------- + --------------------------------- - ----------------------------------------------------------------------------
           5/2                      ______________________               ______________________                                                  3/2                          
        8*x                        /                    2               /                    2                             /                   2\                             
                            ___   /      /      2      \         3/2   /      /      2      \                              |    /      2      \ |                             
                          \/ x *\/   1 - \-1 + x  + 2*x/      2*x   *\/   1 - \-1 + x  + 2*x/                              \1 - \-1 + x  + 2*x/ /
−4x(x+1)(3x2+6x+2(x+1)2−6(x+1)2(x2+2x−1)2(x2+2x−1)2−1−3)(1−(x2+2x−1)2)32+3(2(x+1)2(x2+2x−1)(x2+2x−1)2−1−1)x1−(x2+2x−1)2+3(x+1)2x321−(x2+2x−1)2+3acos⁡(x2+2x−1)8x52- \frac{4 \sqrt{x} \left(x + 1\right) \left(3 x^{2} + 6 x + 2 \left(x + 1\right)^{2} - \frac{6 \left(x + 1\right)^{2} \left(x^{2} + 2 x - 1\right)^{2}}{\left(x^{2} + 2 x - 1\right)^{2} - 1} - 3\right)}{\left(1 - \left(x^{2} + 2 x - 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{3 \left(\frac{2 \left(x + 1\right)^{2} \left(x^{2} + 2 x - 1\right)}{\left(x^{2} + 2 x - 1\right)^{2} - 1} - 1\right)}{\sqrt{x} \sqrt{1 - \left(x^{2} + 2 x - 1\right)^{2}}} + \frac{3 \left(x + 1\right)}{2 x^{\frac{3}{2}} \sqrt{1 - \left(x^{2} + 2 x - 1\right)^{2}}} + \frac{3 \operatorname{acos}{\left(x^{2} + 2 x - 1 \right)}}{8 x^{\frac{5}{2}}}
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Gráfico
Derivada de y=(√x)arccos(x^2+2x-1)
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