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y=sqrt(arccos(x^3+4x))
Derivada de la función/ arccos/ x^3+4/ y=sqrt(arccos(x^3+4x))

Derivada de y=sqrt(arccos(x^3+4x))

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   ________________
  /     / 3      \ 
\/  acos\x  + 4*x/
acos⁡(x3+4x)\sqrt{\operatorname{acos}{\left(x^{3} + 4 x \right)}} 
sqrt(acos(x^3 + 4*x))
Gráfica
02468-8-6-4-2-10105-5
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Trazar el gráfico f'(x)
Primera derivada [src] 
                 /       2\                
                -\4 + 3*x /                
-------------------------------------------
      _________________                    
     /               2     ________________
    /      / 3      \     /     / 3      \ 
2*\/   1 - \x  + 4*x/  *\/  acos\x  + 4*x/
−3x2+421−(x3+4x)2acos⁡(x3+4x)- \frac{3 x^{2} + 4}{2 \sqrt{1 - \left(x^{3} + 4 x\right)^{2}} \sqrt{\operatorname{acos}{\left(x^{3} + 4 x \right)}}}
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Segunda derivada [src] 
                                                  2                              2         
                                        /       2\                     /       2\  /     2\
           3*x                          \4 + 3*x /                   x*\4 + 3*x / *\4 + x /
- ---------------------- + -------------------------------------- - -----------------------
      __________________     /                2\                                        3/2
     /                2      |      2 /     2\ |     /  /     2\\     /               2\   
    /       2 /     2\     4*\-1 + x *\4 + x / /*acos\x*\4 + x //     |     2 /     2\ |   
  \/   1 - x *\4 + x /                                              2*\1 - x *\4 + x / /   
-------------------------------------------------------------------------------------------
                                      __________________                                   
                                     /     /  /     2\\                                    
                                   \/  acos\x*\4 + x //
−x(x2+4)(3x2+4)22(−x2(x2+4)2+1)32−3x−x2(x2+4)2+1+(3x2+4)24(x2(x2+4)2−1)acos⁡(x(x2+4))acos⁡(x(x2+4))\frac{- \frac{x \left(x^{2} + 4\right) \left(3 x^{2} + 4\right)^{2}}{2 \left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{3}{2}}} - \frac{3 x}{\sqrt{- x^{2} \left(x^{2} + 4\right)^{2} + 1}} + \frac{\left(3 x^{2} + 4\right)^{2}}{4 \left(x^{2} \left(x^{2} + 4\right)^{2} - 1\right) \operatorname{acos}{\left(x \left(x^{2} + 4\right) \right)}}}{\sqrt{\operatorname{acos}{\left(x \left(x^{2} + 4\right) \right)}}}
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Tercera derivada [src] 
                                           3                                   3                                                         2           3                                                                  3                
                                 /       2\                          /       2\                     2 /     2\ /       2\      2 /     2\  /       2\                    /       2\                           /       2\  /     2\       
            3                    \4 + 3*x /                        3*\4 + 3*x /                  9*x *\4 + x /*\4 + 3*x /   3*x *\4 + x / *\4 + 3*x /                9*x*\4 + 3*x /                       3*x*\4 + 3*x / *\4 + x /       
- ---------------------- - ----------------------- - ----------------------------------------- - ------------------------ - -------------------------- + -------------------------------------- - ---------------------------------------
      __________________                       3/2                       3/2                                        3/2                          5/2       /                2\                                         2                 
     /                2      /               2\        /               2\                         /               2\           /               2\          |      2 /     2\ |     /  /     2\\     /                2\                  
    /       2 /     2\       |     2 /     2\ |        |     2 /     2\ |        2/  /     2\\    |     2 /     2\ |           |     2 /     2\ |        2*\-1 + x *\4 + x / /*acos\x*\4 + x //     |      2 /     2\ |      /  /     2\\
  \/   1 - x *\4 + x /     2*\1 - x *\4 + x / /      8*\1 - x *\4 + x / /   *acos \x*\4 + x //    \1 - x *\4 + x / /         2*\1 - x *\4 + x / /                                                 4*\-1 + x *\4 + x / / *acos\x*\4 + x //
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                             __________________                                                                                                          
                                                                                                            /     /  /     2\\                                                                                                           
                                                                                                          \/  acos\x*\4 + x //
−3x2(x2+4)2(3x2+4)32(−x2(x2+4)2+1)52−9x2(x2+4)(3x2+4)(−x2(x2+4)2+1)32−3x(x2+4)(3x2+4)34(x2(x2+4)2−1)2acos⁡(x(x2+4))+9x(3x2+4)2(x2(x2+4)2−1)acos⁡(x(x2+4))−(3x2+4)32(−x2(x2+4)2+1)32−3(3x2+4)38(−x2(x2+4)2+1)32acos⁡2(x(x2+4))−3−x2(x2+4)2+1acos⁡(x(x2+4))\frac{- \frac{3 x^{2} \left(x^{2} + 4\right)^{2} \left(3 x^{2} + 4\right)^{3}}{2 \left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{5}{2}}} - \frac{9 x^{2} \left(x^{2} + 4\right) \left(3 x^{2} + 4\right)}{\left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{3}{2}}} - \frac{3 x \left(x^{2} + 4\right) \left(3 x^{2} + 4\right)^{3}}{4 \left(x^{2} \left(x^{2} + 4\right)^{2} - 1\right)^{2} \operatorname{acos}{\left(x \left(x^{2} + 4\right) \right)}} + \frac{9 x \left(3 x^{2} + 4\right)}{2 \left(x^{2} \left(x^{2} + 4\right)^{2} - 1\right) \operatorname{acos}{\left(x \left(x^{2} + 4\right) \right)}} - \frac{\left(3 x^{2} + 4\right)^{3}}{2 \left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{3}{2}}} - \frac{3 \left(3 x^{2} + 4\right)^{3}}{8 \left(- x^{2} \left(x^{2} + 4\right)^{2} + 1\right)^{\frac{3}{2}} \operatorname{acos}^{2}{\left(x \left(x^{2} + 4\right) \right)}} - \frac{3}{\sqrt{- x^{2} \left(x^{2} + 4\right)^{2} + 1}}}{\sqrt{\operatorname{acos}{\left(x \left(x^{2} + 4\right) \right)}}}
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Gráfico
Derivada de y=sqrt(arccos(x^3+4x))
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