Derivada de y=x+√√x/arccos(3x)

Ha introducido [src]

       _____ 
     \/ 4*x  
x + ---------
    acos(3*x)

\frac{\sqrt{4 x}}{\operatorname{acos}{\left(3 x \right)}} + x

x + sqrt(4*x)/acos(3*x)

Gráfica

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Primera derivada [src]

                                   ___        
           1                 3*2*\/ x         
1 + --------------- + ------------------------
      ___                __________           
    \/ x *acos(3*x)     /        2      2     
                      \/  1 - 9*x  *acos (3*x)

\frac{3 \cdot 2 \sqrt{x}}{\sqrt{1 - 9 x^{2}} \operatorname{acos}^{2}{\left(3 x \right)}} + 1 + \frac{1}{\sqrt{x} \operatorname{acos}{\left(3 x \right)}}

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Segunda derivada [src]

                       ___                                                      3/2        
    1             36*\/ x                         6                         54*x           
- ------ - ---------------------- + ----------------------------- + -----------------------
     3/2   /        2\     2                 __________                       3/2          
  2*x      \-1 + 9*x /*acos (3*x)     ___   /        2              /       2\             
                                    \/ x *\/  1 - 9*x  *acos(3*x)   \1 - 9*x /   *acos(3*x)
-------------------------------------------------------------------------------------------
                                         acos(3*x)

\frac{\frac{54 x^{\frac{3}{2}}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{36 \sqrt{x}}{\left(9 x^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x \right)}} + \frac{6}{\sqrt{x} \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} - \frac{1}{2 x^{\frac{3}{2}}}}{\operatorname{acos}{\left(3 x \right)}}

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Tercera derivada [src]

  /                                                     ___                       ___                        3/2                       5/2                                        \
  |  1                   18                        45*\/ x                  108*\/ x                    324*x                     486*x                           3               |
3*|------ - ---------------------------- + ----------------------- + ------------------------ + ----------------------- + ----------------------- - ------------------------------|
  |   5/2     ___ /        2\     2                  3/2                       3/2                         2                        5/2                       __________          |
  |4*x      \/ x *\-1 + 9*x /*acos (3*x)   /       2\                /       2\        3        /        2\      2        /       2\                   3/2   /        2           |
  \                                        \1 - 9*x /   *acos(3*x)   \1 - 9*x /   *acos (3*x)   \-1 + 9*x / *acos (3*x)   \1 - 9*x /   *acos(3*x)   2*x   *\/  1 - 9*x  *acos(3*x)/
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                     acos(3*x)

\frac{3 \left(\frac{486 x^{\frac{5}{2}}}{\left(1 - 9 x^{2}\right)^{\frac{5}{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{324 x^{\frac{3}{2}}}{\left(9 x^{2} - 1\right)^{2} \operatorname{acos}^{2}{\left(3 x \right)}} + \frac{45 \sqrt{x}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{108 \sqrt{x}}{\left(1 - 9 x^{2}\right)^{\frac{3}{2}} \operatorname{acos}^{3}{\left(3 x \right)}} - \frac{18}{\sqrt{x} \left(9 x^{2} - 1\right) \operatorname{acos}^{2}{\left(3 x \right)}} - \frac{3}{2 x^{\frac{3}{2}} \sqrt{1 - 9 x^{2}} \operatorname{acos}{\left(3 x \right)}} + \frac{1}{4 x^{\frac{5}{2}}}\right)}{\operatorname{acos}{\left(3 x \right)}}

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Derivada de y=x+√√x/arccos(3x)

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